EPJ manuscript No. (will be inserted by the editor)

Beta-decay studies for applied and basic nuclear physics

A. Algora1,2, J. L. Tain1, B. Rubio1, M. Fallot3, and W. Gelletly4 1 IFIC (CSIC-Univ. Valencia), Paterna, Spain 2 Institute of Nuclear Research (ATOMKI), Debrecen, Hungary 3 Subatech (CNRS/in2p3 - Univ. Nantes - IMTA), Nantes, France 4 University of Surrey, Surrey, UK

Received: date / Revised version: date

Abstract. In this review we will present the results of recent beta-decay studies using the total absorption technique that cover topics of interest for applications, nuclear structure and astrophysics. The decays studied were selected primarily because they have a large impact on the prediction of a) the decay heat in reactors, important for the safety of present and future reactors and b) the reactor electron anti- neutrino spectrum, of interest for particle/nuclear physics and reactor monitoring. For these studies the total absorption technique was chosen, since it is the only method that allows one to obtain beta decay probabilities free from a systematic error called the Pandemonium effect. The total absorption technique is based on the detection of the gamma cascades that follow the initial beta decay. For this reason the technique requires the use of calorimeters with very high gamma detection efficiency. The measurements presented and discussed here were performed mainly at the IGISOL facility of the University of Jyv¨askyl¨a (Finland) using isotopically pure beams provided by the JYFLTRAP Penning trap. Examples are presented to show that the results of our measurements on selected nuclei have had a large impact on predictions of both the decay heat and the anti-neutrino spectrum from reactors. Some of the cases involve beta- delayed neutron emission thus one can study the competition between gamma- and neutron-emission from states above the neutron separation energy. The gamma-to-neutron emission ratios can be used to constrain neutron capture (n,γ) cross sections for unstable nuclei of interest in astrophysics. The information obtained from the measurements can also be used to test nuclear model predictions of half-lives and Pn values for decays of interest in astrophysical network calculations. These comparisons also provide insights into aspects of nuclear structure in particular regions of the nuclear chart.

PACS. 21.10.Pc Single-particle levels and strength functions – 23.40.s β decay; double β decay; electron and muon capture – 26.50.+x Nuclear physics aspects of novae, supernovae, and other explosive environ- ments – 29.30.h Spectrometers and spectroscopic techniques – 29.90.+r Other topics in elementary-particle and nuclear physics experimental methods and instrumentation

1 Introduction states involved. Thus characteristic alpha and gamma ray spectra exhibit a series of discrete lines. It requires sophis- Our knowledge of the properties of atomic nuclei is derived ticated detection and analysis techniques to determine the almost entirely from studies of nuclear reactions and ra- excitation energies of the states involved, their lifetimes dioactive decays. The ground and excited states of nuclei and the transition rates between states. Beta decay carries arXiv:2007.07918v1 [nucl-ex] 15 Jul 2020 exhibit many forms of decay but the most common are al- the same information, but the difficulties of measurement pha, beta and gamma-ray emission. Our focus here is on and interpretation are compounded because the spectrum beta decay in its various manifestations. A glance at the is continuous, not discrete. In 1930 this was explained by Segre Chart reveals that it is the most common way for Pauli’s hypothesis [1] of the existence of a neutral, zero the ground states of nuclei to decay and it is frequently mass particle called in his letter the neutron that is emit- the observation of such beta decays that brings us our first ted with the beta particle. The sharing of momentum and knowledge of a particular nuclear species and its proper- energy then explains the continuous spectrum. Shortly af- ties. terwards Fermi [2] was able to formulate a theory of beta The study of beta decay is intrinsically much more decay based on this idea and coined the name neutrino difficult than the study of either alpha or gamma decay. (little neutral one) for the particle. The reason for this is straightforward. Alpha particles and A knowledge of beta decay transition probabilities is gamma rays are emitted with discrete energies determined of particular importance for application to a) tests of nu- by the differences in energy between the initial and final clear model calculations, b) the radioactive decay heat in 2 A. Algora et al.: Beta-decay studies for applied and basic nuclear physics

Fig. 2. Simplified picture of a beta decay where only one ex- cited state is populated and it de-excites by the emission of a gamma cascade. The left hand panel represents the case. The Fig. 1. Schematic picture of how the beta feeding is deter- central panel presents the Pandemonium effect, in this example mined in a beta decay experiment employing Ge detectors. represented by missing, or not detecting the gamma transition The beta feeding (Iβ (i)) to level i is determined from the dif- γ2. The right hand panel represents the displacement of the ference of the total intensity feeding the level and those de- beta decay intensity because of the non detection of the tran- exciting it. The sum over (k) represents all transitions feeding sition γ2. or de-exciting the level. Iγk stands for the gamma intensity of transition k and ICEk represents the conversion electron inten- sity. means that we have a problem that has become known as the Pandemonium effect [3] (see Figure 2 for a simplified picture). reactors, c) the reactor electron anti-neutrino spectrum We can overcome this problem using the total absorp- and d) reaction network calculations for nucleosynthesis tion gamma spectroscopy technique, where we take a dif- in explosive stellar events. In this article we will provide ferent approach. The method involves a large 4π scintilla- examples of our recent studies of beta decays that involve tion detector and is based on the detection of the full de- the use of total absorption gamma spectroscopy (TAGS) excitation gamma cascade for each populated level, rather to tackle the topics listed above. The TAGS method was than the individual gamma rays. The power of TAGS to adopted in our measurements because it overcomes the find the missing beta intensity has been demonstrated in difficulties inherent in the conventional use of Ge detector a number of papers [4,5,6,7,8,9,10,11,12,13]. The use of arrays for this purpose. Such arrays are an important and the TAGS method began at ISOLDE[14]. Its development essential tool for constructing nuclear decay schemes since and history are described in [15,16]. they are very well suited to the study of gamma-gamma Looking at a wider picture we see that many entries coincidences, the main basis for building such schemes. in the international databases, that rely on measurements The normal practice is then to derive beta decay transi- with Ge detectors alone, will have systematic errors. As tion probabilities for each level populated from the differ- we shall see in the sections that follow this means that ence in the total intensity of all the gamma rays feeding the results cannot be relied on for certain applications. the level and the sum of the intensities of all those de- The answer to the resulting difficulties lies in the use of exciting it, corrected by the effect of internal conversion TAGS. In the remainder of this article we will describe (see Figure 1). In principle this allows us to obtain the the TAGS method in more detail and then use our results beta branching to every level, assuming that we are able to illustrate how it can be applied. to determine by some other means the number of decays The structure of this article is the following: in Section that go directly to the daughter ground state, which are 2 details of the experimental method and the analysis of not accompanied by gamma emission. the spectra are described. Sections 3, 4, 5 and 6 deal with Unfortunately this ”simple” procedure does not neces- beta decay studies related to a) radioactive decay heat sarily give us the correct answers. States at high excita- (DH), b) reactor antineutrino spectra c) nuclear models, tion energies in the daughter nucleus can be populated if and d) astrophysical applications respectively. Finally, in the Q value of the decay is large. In this case both the β Section 7, a summary will be presented. number of levels that can be directly populated by the beta decay is large and the number of levels available to which they can gamma decay is also large. As a result, in general, individual gamma rays (emitted by levels at high 2 TAGS measurements excitation energy) have low intensity. Ge detectors, indeed even gamma-ray arrays, have limited detection efficiencies In Section 1 it was already explained why we need TAGS particularly at higher energies and thus weak transitions measurements. Figure 3 shows how the simple beta de- are often not detected in experiments. It is clear that this cay presented in Figure 2 is detected by typical detectors A. Algora et al.: Beta-decay studies for applied and basic nuclear physics 3

in bin i of the TAGS spectrum, fj is the beta feeding to the level j (our goal) and Ci is the contribution of the con- taminants to bin i of the TAGS spectrum. The index j in the sum runs over the levels populated in the daugther nu- cleus in the beta decay. The response matrix Rij depends on the TAGS setup and on the assumed level scheme of the daughter nucleus. The dependence on the level scheme of the daughter nucleus is introduced through the branch- ing ratio matrix B. This matrix contains the information of how the different levels in the assumed level scheme decay to the lower lying levels. To calculate the response matrix Rij(B) the branching ratio matrix B has to be Fig. 3. Schematic picture of how the simple beta decay de- determined first. There are different ways to extract the picted in Figure 2 is seen ideally by different detectors used feeding distribution from equation 1 or, in other words, to in beta decay studies. Left panel, representation of a total ab- solve the TAGS inverse problem. One can assume the ex- sorption detector, rigth panel, ideally detected spectra with a istence of ”pseudo” levels that are added manually (with beta dectector (a silicon detector), a Ge detector and a to- their decaying branches) to the known level scheme, cal- tal absorption detector after the simple decay represented in culate their response and see their effect in the calculated Figure 2. spectrum (see for example [17,18]). In our analysis until now we have followed an alternative way for which the level scheme of the daughter nucleus is divided into two used in beta decay experiments. Because a TAGS detec- regions, a low excitation part and a high excitation part. tor acts like a calorimeter, in an ideal TAGS experiment Conventionally the levels of the low excitation part and the detected spectrum will be proportional to the beta their gamma decay branchings are taken from high reso- intensity distribution. This spectrum is obtained in ideal lution measurements available in the literature, since it is conditions, where there is no penetration of the beta parti- assumed that the gamma branching ratios of these levels cles, or the radiation generated by them, into the detector are well determined. Above a certain energy, the cut-off and the TAGS detector is 100% efficient up to the full en- energy, a continuum of possible levels divided into 40 keV ergy of the gamma rays that follow the beta decay. That bins is assumed. From this energy up to the decay Qβ means that only the full absorption peak corresponding to value, the statistical model is used to generate a branch- the sum energy of the gamma cascade is detected in the ing ratio matrix for the high excitation part of the level − case of a β decay. scheme. The statistical model is based on a level density A real experiment does not quite match this ideal. function and gamma strength functions of E1, M1, and E2 In order to achieve very high detection efficiencies, large, character. Once the branching ratio matrix (B) is defined, close to 4π, detector volumes are needed. Thus inorganic the response of the setup Rij to that branching matrix B scintillation material has been the natural choice. Because (or level scheme) is calculated using previously validated of its good average properties NaI(Tl) has been used in all Monte Carlo simulations of the relevant electromagnetic except one (see later) of the existing spectrometers. Nev- interactions in the experimental setup. The validation of ertheless we need some opening to take the sources to the Monte Carlo simulations is performed by reproducing the centre of the spectrometer, either in the form of a ra- measurements of well known radioactive sources, that are dioactive beam or deposited onto a tape transport system. made under the same experimental conditions as the real The latter may also be needed to remove the sources after experiment. The Monte Carlo simulations require a care- some measuring time. We may also need ancillary detec- ful implementation of all the details of the geometry of tors for detecting coincidences and selecting the events in the setup, a proper knowledge of the materials employed which we are interested. In addition TAGS detectors re- in the construction of the setup and testing to find the quire, in general, some form of encapsulation. All these best Monte Carlo tracking options and physics models requirements mean that we have dead material and holes that reproduce the measured sources. It should be noted in our detector system. Accordingly the gamma detection that from high resolution measurements we use only the efficiency of our system will not be 100%. The consequence branching ratios of the levels, and not the information on is that to obtain the beta intensity distribution we need the feeding of these levels. to solve the inverse problem represented by the following equation: Once the response function is determined we can solve jmax X Equation 1 using appropriate algorithms to determine the d = R (B)f + C (1) i ij j i feeding (or beta intensity) distribution. In our analyses we j=0 follow the procedure developed by the Valencia group. In where di is the content of bin i in the measured TAGS [19] several algorithms were explored. From those that are spectrum, Rij is the response matrix of the TAGS setup possible, the expectation maximization (EM) algorithm is and represents the probability that a decay that feeds level conventionally used, since it provides only positive solu- j in the level scheme of the daughter nucleus gives a count tions for the feeding distributions and no additional reg- 4 A. Algora et al.: Beta-decay studies for applied and basic nuclear physics ularization parameters (or assumptions) are required to normally used to isolate the nucleus of interest. On-line solve the TAGS inverse problem. mass separators are used with low energy radioactive beams Clearly, the first level scheme (or defined branching ra- to reduce the contamination represented by mass isobars. tio matrix) considered is not necessarily the one that will In-flight separation is used at high-energy fragmentation provide a nice description of the measured TAGS spec- facilities to reduce the number of nuclear species in the trum. For that reason, as part of the analysis the cut-off ”cocktail beam” to suitable levels. Even if we can isolate energy and the parameters that define the branching ra- the nucleus of interest, daughter (and other descendants) tio matrix can be varied until the best description of the activity can contaminate the measured spectrum depend- experimental data is obtained. Also assumptions on the ing on the half-life of the studied decay. This contamina- spin and parity of the ground state of the parent nucleus tion can be determined through dedicated measurements and on the spins and parities of the populated levels can on the decay of the contaminant nuclei under the same be changed when they are not known unambigously, since conditions as the one of interest. Another source of con- to connect the levels in the continuum to levels in the tamination of the spectrum is the pile-up of signals. The known part of the level scheme we need information about pile-up can distort the full TAGS spectrum and can gen- their spin and parity. All these changes provide different erate counts in regions of the spectra where there should branching ratio matrices (or daughter level schemes) that not be counts, as for example in the region beyond the are considered during the analysis and for all of them the Qβ value of the decay. Also it can distort the spectrum in corresponding response matrixes are calculated and Equa- regions where we expect reduced statistics as for example tion 1 is solved. The final analysis is then based on the close to the Qβ value of the decay. This is the reason why level scheme (or branching ratio matrix) that is consis- estimating this contribution is of importance. Algorithms tent with the available information from high resolution have been developed to evaluate this contribution [21,22]. measurements and at the same time provides the best de- Its determination is based on the random superposition scription of the experimental data. So in practical terms of true detector pulses, measured during the experiment, the following steps are followed until the best description within the time interval defined by the acquisition gate of of the data is obtained: a) define a branching ratio matrix the data acquisition system. B, b) calculate the corresponding response matrix Rij(B), and c) solve the corresponding Equation 1 using an appro- Another possible contamination appears when the de- priate algorithm d) compare the generated spectrum after cay is accompanied by beta delayed particle emission, since the analysis (R(B)f +C) with the experimental spectrum this process can lead promptly to the emission of gamma d. rays from the final nucleus populated by the beta delayed We have only mentioned briefly how the response func- particle emission. The case of the emission of beta de- tion Rij(B) is calculated. More specifically the response layed neutrons is even more complex. Neutrons interact for each level can be determined recursively starting from easily with the detector material and release their energy the lowest level in the following way [20]: through inelastic and capture processes. The proper eval- uation of this contamination is of great relevance in the j−1 study of beta decays far from stability on the neutron-rich X side of the Segre chart and requires careful Monte Carlo Rj = bjkgjk ⊗ Rk (2) k=0 simulations of the neutron-detector interactions [22,23]. The reproduction of this contamination is complicated be- where Rj is the response to level j, gjk is the response cause it has two components: one, which is prompt with of the gamma transition from level j to level k which is cal- the beta decay, is composed of gamma rays emitted in the culated using Monte Carlo simulations, bjk is the branch- final nucleus after the beta-delayed neutron emission when ing ratio for the gamma transition connecting level j to an excited state is populated, the other component due to level k, and Rk is the response to level k. Here the index neutron interactions in the detector is delayed, since the k runs for all the levels below the level j. For simplicity speed of neutrons is much lower than that of gamma-rays. we have not included here in the formula the convolu- To simulate these effects properly an event generator [24], tion with the response of the beta particles and only the that takes into account relative contribution of the two gamma part of the response is presented. Note that in this components is required. It is also necessary to know the last notation Rj is a vector that contains as elements the energy spectrum of the emitted beta-delayed neutrons. In Rij matrix elements mentioned above for all possible i-s addition, the Monte Carlo simulation code should include (or channels) of the TAGS spectrum and the branching an adequate physics model of the neutron interactions. As ratio matrix enters in the formula of the response matrix an example, in Figure 4 [25] the contribution of the cal- through the decay branches bjk-s. In the real calculation of culated beta delayed neutron contamination to the TAGS the responses the internal conversion process is also taken decay spectrum of 95Rb is presented. Two available neu- into account. tron energy spectra were used in the simulations [26,27], Prior to the analysis, the contaminants in the TAGS and clearly only one reproduces the experimental TAGS spectrum (Ci) have to be isolated and their individual data at high excitation energies. This figure shows the rel- contributions evaluated. The nucleus to be studied is pro- evance of the neutron spectrum used in the simulations duced by nuclear reactions together with a number of ad- (for more details see [25]). Due to these complications we ditional nuclei. Two alternative separation methods are have built Rocinante [24,28] a spectrometer made of BaF2 A. Algora et al.: Beta-decay studies for applied and basic nuclear physics 5

delayed neutrons, this contribution can be normalized to 4 95 10 Rb → 95Sr the broad high-energy structure generated by neutron cap- TAGS spectrum: tures in the detector material when possible, otherwise it 3 Experiment should be normalized to the Pn value of the decay. 10 837 keV Counts MC with In from Kratz In Figure 5, we present as an example a total absorp- MC with In from ENSDF tion spectrum measured during our first experiment in 102 Jyv¨askyl¨aof the decay of 104Tc [7,8] which is relevant for the decay heat application (see Section 3). In the upper Neutron panel of this figure we show the spectrum of this decay 10 capture compared with the reproduction of the spectrum after the analysis and the contribution of the contaminants (back- 1 ground+daughter activity+pileup). In this measurement a TAGS detector that consisted 0 2000 4000 6000 8000 10000 of two NaI(Tl) cylindrical crystals with dimensions: = Energy [keV] 200 mm × l = 200 mm, and = 200 mm × l = 100 mm Fig. 4. Impact of the neutron energy spectrum (In) in the was used (courtesy of Dr. L. Batist). The longer crystal simulations of the contamination associated with the beta de- has a longitudinal hole of = 43 mm for the positioning layed neutrons in the TAGS spectrum (for more details see of the sources in the approximate geometrical centre of [25]). Only the spectrum measured by Kratz et al. [26] re- the spectrometer using a tape system. In the experiment produces the TAGS spectrum at high excitation energies. The the crystals were separated by 5 mm. This separation and Monte Carlo (MC) spectra are normalized to the experimental the ideal position of the sources inside the spectrometer spectrum around the neutron capture peak indicated with an was studied previous to our experiment using Monte Carlo arrow. The prompt 836.9 keV γ-ray peak from the first excited simulations in order to maximize the gamma efficiency of state in the final nucleus after the beta-delayed neutron emis- 94 the setup [29]. This TAGS had a 57% peak and 92% to- sion Sr is highlighted. Reprinted figure with permission from tal efficiency for the 662 keV gamma transition emitted [25], Copyright (2019) by the American Physical Society. in 137Cs decay and 27% peak and 70% total efficiency for a 5 MeV gamma transition. This last value was obtained from previously validated Monte Carlo simulations. The material, aimed at the measurement of beta-delayed neu- efficiency of this setup is modest compared with recently tron emitters. BaF has a neutron capture cross-section 2 developed total absorption spectrometers such as DTAS one order-of-magnitude smaller than the NaI(Tl), that is [30], or MTAS [31]. This detector was designed at the Nu- conventionally used. This spectrometer was also the first clear Institute of St. Petersburg (Russia) [32]. of a new generation of segmented devices designed to ex- ploit the cascade multiplicity information to improve the This measurement was analyzed in singles, since the TAGS analysis, as will be mentioned later. precision and reproducibility of the tape positioning sys- It is important to first identify the different distor- tem was considered not sufficiently good to allow coinci- tions or contaminations, but it is also important to deter- dence counting. The positioning of the sources is critical mine properly their corresponding weight in the measured in the determination of the efficiency of the Si detector spectrum. Depending on the distortion, different strategies used as an ancilliary detector for coincidences with the have been followed. For example, the contribution from beta particles emitted in the decay. The efficiency of the contaminant decays can be evaluated if there is a clear beta detector as a function of end-point energy has a di- peak identified in the spectrum that comes from this con- rect impact on the normalization of the combined beta- tamination that can be used for normalization. Another gamma cascade response of the spectrometer (Rij). Using option is the assessment of this contribution from the so- singles has the advantage of providing much higher statis- lution of the Bateman equations, using the information tics in the analysis compared with gated spectra. However, on half-lives and measurement conditions (collection and the use of gated spectra is preferred, eventually unavoid- measuring cycle times). In the case of high-energy frag- able, in order to reduce contamination from ambient back- mentation experiments where the contamination is due to ground and the selection of events of particular interest. beta-gamma events uncorrelated with the implanted ion it The lower panel of Figure 5 shows the feeding dis- can be evaluated from correlations backward in time. The tribution deduced for the 104Tc decay obtained from the pileup distortion can be evaluated based on the number of TAGS measurement compared with the distribution ob- counts in the TAGS spectra which lie beyond the highest tained from high resolution measurements. From the fig- Qβ value in the decay chain and which are clearly above ure it is clear that the feeding distribution obtained with the contribution of the background, since we can assume the TAGS is shifted to higher energies in the daughter that those counts can only come from this contribution. nucleus, which is typical of a case suffering from the Pan- When this option is not possible because of inadequate demonium effect [7,8,33]. Similar measurements will be statistics, a procedure is given in [21] for the normalisa- discussed in more detail in Section 3. tion of this contribution based on the counting rate and As mentioned earlier, in this measurement a detector the length of the analogue to digital converter (ADC) gate. was used that was composed of two crystals. The new gen- And finally if there is a contamination arising from beta- eration of available detectors such as Rocinante [24], SUN 6 A. Algora et al.: Beta-decay studies for applied and basic nuclear physics

[34], MTAS [31] and DTAS [30] exploit segmentation to a : analysis+contaminants 106 : experimental data greater degree to extract additional information from the : contaminants Counts decay under study. Using the segmentation it is possible 5 10 to measure the detector fold (number of detectors fired in an event) which is related to gamma-cascade multiplicity 104 as a function of excitation energy and ultimately to the de-excitation branching ratio matrix B. The lack of knowl- 0 1 2 3 4 5 6 E [MeV] edge of the matrix B is the largest source of uncertainty in : TAGS measurement TAGS analysis and this can be greatly improved with seg- 15 : High resolution measurements Feeding mented detectors. Our current approach to the iterative 10 procedure for updating B described earlier in this Sec- tion, is to include in step d) the comparison to fold-gated 5

TAGS spectra and single module spectra. Reconstructed 0 fold-gated spectra are obtained by MC simulation using 0 1 2 3 4 5 6 Ex (MeV) the appropriate event generator since it is not possible to Fig. 5. Comparison of the measured TAGS spectrum of the define a fold-gated response in a manner similar to Equa- 104 tion 2. This also prevents us from including them as part decay of Tc with the spectrum generated after the analysis of the inverse problem (Equation 1). A different approach (reconstructed spectrum). This last spectrum is obtained by multiplying the response function of the decay with the de- has been taken by the ORNL group to analyze MTAS data termined feeding distribution (R(B)f final). The lower panel [35,36]. They use the coincidence between one module and shows the beta-decay feeding distribution obtained compared the sum of all the modules to define total energy gated sin- with that previously known from high resolution measurements gle detector spectra that are fitted by the sum of a number [7,8,33]. Reprinted figure with permission from [7], Copyright of de-excitation cascades, usually taken from high resolu- (2010) by the American Physical Society. tion spectroscopy and supplemented when necessary with ”pseudo” levels with guess branching ratios and modified iteratively until the best reproduction is achieved. Yet an- other approach is used by the NSCL group to extract B from SUN data [37]. They start from the same total en- results, revealing that this decay did not suffer seriously ergy gated single detector spectra but apply the so called from the Pandemonium systematic error (see Figure 7). Oslo-method [38] to obtain the branching ratio matrix for This decay is not only important in the framework of dou- a subset of levels. Because of this, the TAGS analysis is ble beta decay studies, it has also recently attracted atten- not performed with this B but uses the ”pseudo” level ap- tion in another neutrino related topic [42]. The decay is a proach including in the fit the total absorption spectrum relevant contributor in a newly identified flux-dependent and the spectrum of detector multiplicities [39]. It should correction to the antineutrino spectrum produced in nu- be noticed that the traditional Oslo method is not strictly clear reactors that takes into account the contribution of applicable to TAGS data because the assumed equivalence the decay of nuclides that are produced by neutron cap- of total deposited energy with excitation energy does not ture of long lived fission products. In this particular case hold in general, due to the non-ideal detector response. 99Tc is produced as a fission product, which after neutron Currently we are working in a method to solve the full capture becomes 100Tc that beta decays. The effect has a non-linear inverse problem represented by Equation 1, to nonlinear dependence on the neutron flux, because first a obtain feedings and branching ratios from the complete fission is required and later a neutron capture. Effects like data set provided by a segmented spectrometer: sum en- this one are considered in order to explain features of the ergy spectrum gated by detector fold, sum energy spec- predicted antineutrino spectrum for reactors not yet fully trum versus single crystal spectrum and crystal-crystal understood (see Section 4). correlations. The study of this decay was the first time that the In Figure 6 we show the spectrum of the beta decay DTAS detector was used at a radioactive beam facility. of 100Tc measured in a recent campaign of measurements Prior to the analysis of this case a full characterization at the IGISOL IV facility of the Univ. of Jyv¨askyl¨a[40, of the detector was performed [22,40]. This included a 41] with the segmented DTAS detector. This single de- check on the ability to reproduce with MC simulations cay is part of the A=100 system of relevance for double the spectrum of decays obtained with different detector beta decay studies (100Ru - 100Tc - 100Mo). Previous to multiplicity (fold) conditions. As an example we present this study, only a high resolution measurement existed in Figure 8 the reproduction of the multiplicities for the for this single decay and there were doubts whether feed- 22Na source used in the characterization of the detector. ing at high excitation energy is not detected in the high The DTAS is constructed in a modular way that adds resolution measurements. Single decays, like this one can extra versatility to the setup [30]. Depending on the in- be of relevance for fixing model parameters used in the- stallation, it can be used in an 18 detector configuration oretical calculations for neutrino and neutrinoless double for ISOL type facilities or in an 16 detector configuration beta decay studies. Our TAGS results show only a modest for fragmentation facilities, where the positioning of the improvement with relation to the earlier high resolution implantation detectors normally requires more space. A. Algora et al.: Beta-decay studies for applied and basic nuclear physics 7

Fig. 8. Comparison of the measured spectrum of the decay of 22Na with different multiplicity conditions on the number of detectors that fired (fold) with the results of Monte Carlo Fig. 6. Comparison of the measured TAGS spectrum of the simulations for the DTAS detector [22,40]. How well the differ- decay of 100Tc with the spectrum generated after the analy- ent multiplicity spectrum is reproduced, is a stringent test of sis (reconstructed spectrum). Reprinted figure with permission the quality of the branching ratio matrix used in the analysis. from [41], Copyright (2017) by the American Physical Society. Modified figure with permission from [22], Copyright (2018) by Elsevier.

102 (design of a reactor, storage of the nuclear waste, loss of DTAS

[%] 10 coolant accident (LOCA), etc.). β

I ENSDF Decay heat is defined as the amount of energy released 1 by the decay of fission products not taking into account 10−1 the energy taken by the neutrinos. The first method to es- timate the decay heat was introduced by Way and Wigner −2 10 [44], which was based on statistical considerations of the 10−3 fission process. Their results provide a good estimate of the heat released, but the precision reached is not sufficient 10−4 for present-day safety standards. Nowadays the most ex- 0 500 1000 1500 2000 2500 3000 Energy [keV] tended way to estimate the decay heat is to perform sum- mation calculations, which relies on the increased amount Fig. 7. Comparison of the obtained TAGS feeding distribution 100 of available nuclear data. In this method, the power func- in the decay of Tc with the data available from high reso- tion of the decay heat f(t) is obtained as the sum of the lution measurement. This is an example of a case that did not activities of the fission products times the energy released suffer from the Pandemonium effect. Reprinted figure with per- mission from [41], Copyright (2017) by the American Physical per decay: Society. X f(t) = (Eβ,i + Eγ,i)λiNi(t) (3) i 3 Decay heat where Ei is the mean decay energy of the ith nuclide Nuclear reactor applications require beta decay data. The (β or charged-particle and γ or electromagnetic compo- relevance of beta decay is shown by the fact that each nents), λi is the decay constant of the ith nuclide, and fission is followed by approximately six beta decays. The Ni(t) is the number of nuclides of type i at the cooling energy balance released in fission is presented in Table 1 time t (for simplicity the α-decays of minor actinides are for 235U and 239Pu fissile isotopes [43]. In the case of 235U, not included here). These calculations require extensive for example, 7.4 % of the energy released comes from the libraries of cross sections, fission yields and decay data, beta decay of the fission products (FP) (gamma and beta since the method first requires the solution of a system of energy). Depending on the composition of the fuel in the coupled differential equations to determine the inventory reactor this percentage can change, but it is of the order of of nuclei Ni(t) produced in the working reactor and after 7% of the total released energy for a working reactor. Once shut-down. the reactor is shut-down, the decay energy becomes dom- Several ingredients of this method depend on decay inant and the related heat has to be removed. If for some data. The determination of the activities of the fission reason this is not possible, it can produce accidents like products (λiNi(t)) requires a knowledge of the half-lives the one caused originally by the tsunami that followed the of the decaying isotopes. The other important quantities Great East Japan Earthquake (2011) in the Fukushima are the mean energies released per decay (Eβ,i, Eγ,i). The Daiichi power plant. Clearly one needs to estimate this mean energies released per decay i can be obtained by source of energy for the safety of any nuclear installation direct measurements as in the systematic studies by Rud- 8 A. Algora et al.: Beta-decay studies for applied and basic nuclear physics

Table 1. Division of the energy released by the most important Table 3. List of parent nuclides identified in [50] that should be fissile isotopes 235U and 239Pu (values given in MeV/fission) measured using the total absorption technique to improve the [43]. predictions of the decay heat in reactors based on 233U/232Th fuel. The list does not contain several relevant cases already Contribution 235U 239Pu measured by [17] and already included in Table 2 (marked with †), for more details see [50]. Rel. (relevance) stands for the Fragments’ kinetic energy 166.2(13) 172.8(19) priority of the measurement. Isotopes marked with asterisks Prompt neutrons 4.8(1) 5.9(1) show the measurements performed by our collaboration. For Prompt gamma rays 8.0(8) 7.7(14) more details in the notation see Table 2. Beta energy of fission fragments 7.0(4) 6.1(6) Gamma energy of fission fragments 7.2(13) 6.1(13) Isotope Rel. Isotope Rel. Isotope Rel. Subtotal 192.9(5) 198.5(8) 34-Se-85 1 38-Sr-92 2 51-Sb-128m 2 Energy taken by the neutrinos 9.6(5) 8.6(7) 34-Se-86 2 39-Y-96m∗ 1 51-Sb-129m 2 Total 202.7(1) 207.2(3) 35-Br-84 2 39-Y-97 1 51-Sb-130m 1 35-Br-89 1 40-Zr-98 1 51-Sb-133 2 36-Kr-87 2 41-Nb-99m 2 54-Xe-138 1 36-Kr-91 1 41-Nb-100m∗ 1 56-Ba-139 2 37-Rb-88 2 41-Nb-102m∗ 1 57-La-141 2 Table 2. List of parent nuclides identified by the WPEC-25 37-Rb-94∗ 1 42-Mo-101 1 57-La-146m 2 (Nuclear Energy Agency working group) that should be mea- sured using the total absorption technique to improve the pre- dictions of the decay heat in reactors [48,49]. These nuclides are of relevance for conventional reactors based on 235U and available, then it is possible to deduce the mean energies 239Pu fission. The list contains 37 nuclides. Rel. (relevance) released by the decay using the following relations: stands for the priority of the measurement. Isotopes marked with asterisks show the measurements performed by our col- laboration. Nuclides marked with † are also relevant for the X Eγ = Ij ∗ Ej, (4a) 233U/232Th fuel, see additional cases in Table 3. The isotopes j are identified according to the Z-Symbol-A notation; m stands X for metastable or isomeric state. Eβ = Ij∗ < Eβ >j, (4b) j Isotope Rel. Isotope Rel. Isotope Rel.

†∗ † † 35-Br-86 1 41-Nb-99 1 52-Te-135 2 where Ej is the energy of the level j in the daughter †∗ †∗ † 35-Br-87 1 41-Nb-100 1 53-I-136 1 nucleus, Ij is the probability of a beta transition to level †∗ †∗ † 35-Br-88 1 41-Nb-101 1 53-I-136m 1 j, and < Eβ >j is the mean energy of the beta continuum 36-Kr-89† 1 41-Nb-102†∗ 2 53-I-137†∗ 1 populating level j. As can be seen from the formula the 36-Kr-90† 1 42-Mo-103†∗ 1 54-Xe-137† 1 mean gamma energy is approximated by the sum of the 37-Rb-90m 2 42-Mo-105∗ 1 54-Xe-139† 1 energy levels populated in the decay weighted by the beta 37-Rb-92†∗ 2 43-Tc-102†∗ 1 54-Xe-140† 1 transition probability. This approximation assumes that 38-Sr-89 2 43-Tc-103†∗ 1 55-Cs-142∗ 3 each populated level decays by gamma deexcitation and 38-Sr-97 2 43-Tc-104†∗ 1 56-Ba-145 2 ignores conversion electrons which are taken into account 39-Y-96† 2 43-Tc-105∗ 1 57-La-143 2 in the complete treatment of the mean energy calculations. 40-Zr-99† 3 43-Tc-106∗ 1 57-La-145 2 The mean beta energy, because of the continuum charac- 40-Zr-100† 2 43-Tc-107∗ 2 ter of the beta distribution emitted in the population of 41-Nb-98†∗ 1 51-Sb-132† 1 each level, requires the determination of the released mean energy < Eβ >j for each end-point energy of the beta transition (Qβ − Ej). Then the mean beta energy (Eβ) is obtained as the weighted sum of the mean beta energies populating each level by the beta transition probability. stam et al. [45] and Tengblad et al. [46]. These integral For the determination of < Eβ >j for each level one needs measurements (energy per decay) require specific setups to make assumptions about the type of the beta transi- that are only sensitive to the energy of interest and a tion (allowed, first forbidden, etc.) and the knowledge of careful treatment of all possible systematic errors. Alter- the Qβ value of the decay is needed to determine the beta natively the mean energies can be deduced from available transition end-points. decay data in nuclear databases such as the Evaluated Nu- Pandemonium can have an impact in the determina- clear Structure Data File (ENSDF) [47] if the decay prop- tion of the mean energies from data available in databases. erties are properly known. The term ”properly known” If the beta decay data suffers from the Pandemonium ef- beta decay implies a knowledge of the Qβ value of the de- fect the beta decay probability distribution is distorted. cay, the half-life, the beta distribution probability to the This distortion, which implies increased beta probability levels in the daughter nucleus and the decay branching to lower lying levels in the daugther nucleus, causes an ratios of the populated levels. If all this information is underestimation of the mean gamma energy and an over- A. Algora et al.: Beta-decay studies for applied and basic nuclear physics 9 estimation of the mean beta energy. This is why TAGS as a high resolution mass separator for trap assisted spec- measurements are relevant to this application. troscopy measurements, providing a mass resolving power M In fission more than 1000 fission products can be pro- ( ∆M ) of the order of 100 000 to be compared with the duced. But not all of them are equally important. When resolving power of approximately 500 of the IGISOL sep- addressing a particular problem, like the decay heat, it is arator magnet. The purity of the beams is particularly of interest to identify which are the most relevant con- important for calorimetric measurements like those with tributors among the large number of fission products. A TAGS since it reduces systematic errors that can be as- group of experts working for the International Atomic En- sociated with contamination of the primary radioactive ergy Agency (IAEA) [48] identified high priority lists of beams. This advantage has also been used in other types nuclei that are important contributors to the decay heat of calorimetric measurements at IGISOL such as the mea- 3 in reactors and that should be measured using the TAGS surements of beta delayed-neutrons using He counters technique. These lists included nuclides that are produced embedded in a polyethylene matrix [54]. with high yields in fission and for which the decay data Three experimental campaigns have been performed was suspected of suffering from the Pandemonium effect. at the IGISOL facility to study the beta decay of impor- One argument used for this last selection was if the decay tant contributors to the decay heat and to the antineu- data shows no levels fed in the daughter nucleus in the trino spectrum in reactors using the TAGS technique [55, upper 1/3 excitation energy window of the Qβ value. It is 56,57,58]. One of the total absortion setups used in the worth noting that this can be considered only as an indi- experiments is presented in Figure 9 (Rocinante TAGS). cation of Pandemonium and not a rigorous rule. Another In a typical experiment, the radioactive beam extracted way of looking for questionable (or odd) data was to look from IGISOL is first mass separated using the separator for cases that show different mean energies in the different magnet and then further separated using the JYFLTRAP international databases. The final lists were published in Penning trap. Then the beam is transported to the mea- two separate reports, first for U/Pu fuels [49] and then suring position, at the centre of the total absorption spec- later for the possible future Th/U fuel [50]. trometer where it is implanted in a tape from a tape trans- In 2004 we started a research programme aimed at port system. The tape is moved in cycles, which are opti- studying the beta decay of nuclei making important con- mized depending on the half-life of the decay of interest. tributions to the decay heat in reactors. For the planning As mentioned earlier, the reason for using a tape trans- of any nuclear physics experiment the first step is to decide port system is to reduce the effect of undesired daughter, the best facility to perform it in terms of the availability of grand-daughter, etc., decay contaminants in the measured the beams, their cleanness and their intensity. Since some spectrum. If necessary, these contaminants have to be sub- of the most important contributors to the priority list for stracted from the measured TAGS spectrum and require 235U and 239Pu fission were refractory elements like Tc, dedicated measurements. In this kind of measurement the Mo and Nb, the options were very limited. In a classical TAGS detector is usually combined with a beta detector ISOL facility like ISOLDE, the development of a particu- as shown in the inset to the Figure 9. The beta detector is lar beam can take some time if the beam of a particular used to select coincidences of the beta particles with the element is not available. It is a lengthy and complex task TAGS spectrum, which essentially eliminates the effect of to find the optimum chemical and physical conditions in the ambient background. the ion source for the extraction of a particular element. In Figure 10 we show an example of the recently mea- We decided that the best option concerning the availabil- sured 86Br decay, which was considered priority one for ity of the beams was to perform the measurements at the the decay heat problem. The spectrum shows the TAGS IGISOL facility in Jyv¨askyl¨a(Finland) [51]. The reason spectrum obtained with the beta-gate condition, and the for that was the development of the ion-guide technique. contribution of the different contaminants. The analysis The ion-guide technique, and more specifically the fission was performed as described earlier. Known levels up to ion guide, allows the extraction of fission products inde- the excitation value of 3560 keV were taken from the com- pendently of the element. In this technique, fission is pro- piled high resolution data from [59]. From 3560 keV to duced by bombarding a thin target of natural U with a the Qβ=7633(3) keV value, the statistical model is used proton beam. The fission products that fly out of the tar- to generate a branching ratio matrix using a level den- get are stopped in a gas and transported through a differ- sity function resulting from a fit to levels from [60] and ential pumping system into the first accelerator stage of corrected to reproduce the level density at low excita- the mass separator. The dimensions of the ion guide and tion energy, and E1, M1, and E2 gamma strength func- the pressure conditions are optimized in such a way that tions taken from [61]. For more details see [62,63]. In Fig- the process is fast enough for the ions to survive as singly ure 10 we also show the comparison of the beta gated charged ions. As a result the system is chemically insen- TAGS spectrum with the results from the analysis. The sitive and very fast (sub-ms) [52] allowing the extraction reconstructed spectra are obtained by multiplying the re- of any element including those that are refractory. sponse function of the detector with the final feeding dis- Another important advantage of performing experi- tribution obtained from the analysis. In this particular ments at IGISOL is the availability of the JYFLTRAP case two results are presented. Response A corresponds to Penning trap [53] developed for high precision mass mea- the conventionally calculated branching ratio matrix that surements at this facility. JYFLTRAP can also be used fits better the experimental spectrum. Response B corre- 10 A. Algora et al.: Beta-decay studies for applied and basic nuclear physics

100 β Feeding A [%] β

I 90 β Feeding B

∑ ENSDF β feeding 80 70 60 50 40 30 20

0 2000 4000 6000 8000 Energy [keV] Fig. 11. Comparison of the accumulated feeding distributions obtained in the work of Rice et al. [62] for the decay of 86Br with available high resolution measurements. Feeding A and B stands for the TAGS feedings determined. For more details see the text. Reprinted figure with permission from [62], Copyright (2017) by the American Physical Society. Fig. 9. Schematic picture of the Rocinante total absorption spectrometer used in one of the experiments performed at the IGISOL facility of the University of Jyv¨askyl¨a.The spectrom- sponds to a modified branching ratio matrix to reproduce eter is composed of 12 BaF2 crystals. In the lower part the the measured gamma-ray intensities de-exciting each level endcap with the Si detector is also presented (not in scale). as measured in high resolution experiments. In Figure 11 The thick black lines represent the tape used to move away the the feeding distributions obtained are compared with the remaining activity and the blue line represents the direction of available high resolution measurements. This comparison the pure radioactive beam that is implanted in the centre of shows that 86Br decay was suffering from the Pandemo- the spectrometer. Reprinted figure with permission from [24], nium effect. Copyright (2017) by the American Physical Society. In Table 4 we show a summary of the mean energies deduced from TAS analyses obtained in our measurements β•gated performed at Jyv¨askyl¨a.It shows that most of the cases 3 Response A 10 Response B Pile•up addressed from the high priority list were suffering from Counts Background the Pandemonium effect. Two cases, that originally were 102 suspected to be Pandemonium cases (102Tc, 101Nb), were not. Those cases also show the necessity of the TAGS measurements to confirm the suspicion of Pandemonium. 10 Clearly the non existence of feeding in the last Qβ/3 exci- tation is a good indicator to select cases, but it is not 0.21 always conclusive. The 102Tc, 101Nb cases have strong 0 −0.20 2000 4000 6000 8000 ground state feedings, which reduces the impact of the

Rel. dev. 0 2000 4000 6000 undetected gamma branches at high excitation. This is Energy [keV] clearly reflected in the differences of the deduced mean en- Fig. 10. Relevant histograms used in the analysis of the beta ergies, when they are compared with the mean energies de- decay of 86Br: measured spectrum (squares with errors), recon- duced from high resolution data. The values for one-third structed spectrum response A (red line), reconstructed spec- of the Qβ-value (Qβ/3) are also given for comparison with trum response B (blue line), summing-pileup contribution (or- the mean energies. The Qβ/3 value is an approach some- ange line), background (green line). In the lower panel the rel- times used by databases, when there is lack of experimen- ative differences of the experimental spectrum vs the recon- tal data, which in practical terms divides the available de- structed spectrum are shown. Response A corresponds to the cay energy in equal parts between the mean gamma, beta conventional analysis. Response B corresponds to a modified and antineutrino energies. In the table the mean energies branching ratio matrix to reproduce the measured gamma-ray deduced from the high resolution data (ENDSF database) intensities. For more details see Rice et al. [62]. Reprinted figure are also given for comparison [64]. with permission from [62], Copyright (2017) by the American Physical Society. Our results can also be compared where possible with the results of Greenwood et al. [17] and Rudstam et al. [45]. Greenwood and co-workers performed a systematic study of fission products at the Idaho National Engineer- ing Laboratory (INEL), Idaho Falls, USA, using a 252Cf source and the He-jet technique. They employed a total absorption spectrometer built of NaI(Tl) with the follow- ing dimensions, 25.4 cm ×30.5 cm length with a 5.1 cm × A. Algora et al.: Beta-decay studies for applied and basic nuclear physics 11

Table 4. Mean gamma and beta energies deduced from our analyses of beta decays studied at Jyv¨askyl¨ain comparison with the values deduced from high resolution measurements 0.5 (ENSDF database). The highest level identified in the decay studies using high resolution and the decay Q values are also (MeV) β γ given for completeness (for more details see the text). E 0 ∆ HR T AGS HR T AGS Isotope High. Lev. Qβ Qβ /3 Eγ Eγ Eβ Eβ 86Br 6768 7633(3) 2544 3360(110) 3782(116) 1900(300) 1687(60) 87 +40 +32 Br 5793 6818(3) 2273 3100(40) 3938(−67) 1660(80) 1170(−19) −0.5 88 +78 +32 Br 6999 8975(4) 2992 2920(50) 4609(−67) 2240(240) 1706(−38) 91Rb 4793 5907(9) 1969 2270(40) 2669(95) 1580(190) 1389(44) 92Rb 7363 8095(6) 2698 170(9) 461(14) 3640(30) 3498(105) 94 +62 +32 Rb 6064 10281(8) 3427 1750(50) 4063(−66) 2020(90) 2450(−30) 95 +17 +18 0 2 4 6 8 10 Rb 4661 9284(21) 3095 2050(40) 3110(−38) 2320(110) 2573(−8 ) 100gsNb 3130 6384(21) 2128 710(40) 959(318) 2540(210) 2414(154) Q (MeV) 100mNb 3647 6698(31) 2233 2210(60) 2763(27) 2000(200) 1706(13) β 101Nb 1099 4569(18) 1523 270(22) 445(279) 1800(300) 1797(133) 102gsNb 2480 7210(40) 2403 2090(100) 2764(57) 2280(170) 1948(27) Fig. 12. Differences between the mean gamma energies ob- 102mNb 1245 7304(40) 2435 1023(170) 2829(82) 105Mo 2766 4953(35) 1651 551(24) 2407(93) 1900(120) 1049(44) tained with TAGS measurements (see Table 5 and the text 102Tc 2909 4532(9) 1511 81(4) 106(23) 1945(16) 1935(11) for more details) and the direct measurements of Rudstam et 104Tc 4268 5600(50) 1867 1890(30) 3229(24) 1590(70) 931(10) 105Tc 2403 3644(35) 1215 671(19) 1825(174) 1310(210) 764(81) al. [45] after renormalization by a factor of 1.14, which was 106Tc 3930 6547(11) 2182 2190(50) 3132(70) 1900(70) 1457(30) deduced from the comparison of our newly determined mean 107Tc 2680 4820(90) 1607 511(11) 1822(450) 1890(240) 1263(212) 137 +121 +35 91 I 5170 5880(30) 1960 1071(2) 1220(−74 ) 1897(15) 1934(−56) energy for the decay of Rb [62] with that employed by Rud- stam et al. [45]. Blue points represent Greenwood TAGS data and red points represent results from our collaboration. A sys- tematic difference with a mean value of -180 keV remains. 20.3 cm long axial well. The analysis technique employed Reprinted figure with permission from [62], Copyright (2017) in those studies was based on the creation of a level scheme by the American Physical Society. using the information from high resolution measurements and complementing it with the addition of ”pseudo” lev- els by hand when necessary. The response of the detector those decays that were available in both data sets. This was then calculated for the assumed level scheme using comparison was revisited in [66]. A clear systematic differ- the Monte Carlo code CYLTRAN (for more details see ence was shown, pointing to possible systematic errors in [65]). The systematic study of Greenwood et al. provided one or in both data sets [24,62,66]. For that reason it was TAGS data for 48 decays including the decay of three iso- decided to measure the 91Rb decay using the TAGS tech- meric states. Since a different analysis technique was used, nique, to see if the decay was suffering from the Pandemo- it is interesting to compare the results of Greenwood with nium effect or not and accordingly check if this decay was the more recent results and look for possible systematic adequate as an absolute calibration point to obtain mean deviations for cases where the comparison is possible. gamma energies in [45]. The 2669(95) keV mean gamma As mentioned earlier Rudstam et al. performed sys- value obtained from our measurements [62] can be com- tematic measurements of gamma and beta spectra and pared with the value used by Rudstam et al. (2335(33) deduced mean energies [45,46] of interest for the predic- keV) showing that this decay suffered from Pandemonium tion of decay heat. Beta spectra of interest for the predic- and also showing the necessity of renormalizing the Rud- tion of the antineutrino spectrum from reactors were also stam data by a factor of 1.14. With this renormalization, measured [46]. The direct measurements were performed the mean value of the differences between the two data at ISOLDE and at the OSIRIS separator using setups op- sets (TAGS vs Rudstam) reduces from -360 keV to -180 timized for the detection of the gamma- and beta-rays keV, but still the discrepancy remains [62]. This is shown emitted by the fission products. In the case of the mean in Figure 12 and Table 5. It should be noted that our mean gamma energies, the setup required an absolute gamma gamma energy value for this decay agrees nicely with the efficiency calibration with the assumption that the decay value obtained by Greenwood et al. (2708(76) keV) [17]. used in the calibration did not suffer from the Pandemo- In Figs. 13(239Pu) and 14 (235U) the total impact of the nium effect [45]. In their measurements the beta decay total absorption measurements of the 13 decays (86,87,88Br, 91 of Rb was used as a calibration. This decay with a Qβ 91,92,94Rb, 101Nb, 105Mo, 102,104,105,106,107Tc) published of 5907(9) keV shows a complex decay scheme from high in Refs. [7,8,24,62,67] is presented in comparison with resolution measurements that populates levels up to 4700 the decay heat measurements reported by Tobias [68] and keV in the daughter nucleus. So it was assumed naturally Dickens [69] for the electromagnetic component (Eγ ) of by the authors of [45] that this decay was not a Pande- the decay heat. Similarly in Figs. 15-16 the impact of the monium case (in the publication [45] it is mentioned that same decays is compared for the charged particle compo- the gamma spectrum extends up to 4500 keV). nent (Eβ) of the decay heat. To show the impact of the In a contribution to the Working Party on Interna- total absorption measurements the data base JEFF3.1.1 tional Evaluation Co-operation of the NEA Nuclear Sci- is used, in which no total absorption data is included. Cal- ence Committee (WPEC 25) group activities [48], the late culations are performed using the bare JEFF 3.1.1 and a O. Bersillon performed a comparison between the Green- modified version of the JEFF3.1.1 database with the in- wood and Rudstam mean gamma and beta energies for clusion of the total absorption data for the mean energies. 12 A. Algora et al.: Beta-decay studies for applied and basic nuclear physics

Table 5. Comparison of mean gamma energies obtained with T the TAGS measurements (Eγ ) with those obtained in the ded- 0.8 R icated measurements by Rudstam et al. (Eγ ) [45] (original val- ues, not renormalized). Marked with asterisks are our TAGS 0.7 results for the mean energies. The TAGS results not marked with asterisks are taken from Greenwood et al. [17]. 0.6 T R T R Isot. E E Isot. E E γ γ γ γ 0.5 86Br∗ 3782(116) 3420(500) 95Y 1223(50) 1060(120) 87Br∗ 3938(+40) 3560(130) 138mCs 426(27) 500(80) −67 235 88Br∗ 4609(+78) 4290(180) 139Cs 305(8) 299(21) 0.4 U Tobias −67 235 89Rb 2228(145) 1740(40) 140Cs 1864(37) 1270(50) U Dickens 90Rb 2272(79) 1710(50) 141Cs 1708(29) 1140(90) 0.3 JEFF 3.1.1 + TAGS 90mRb 3866(115) 3690(110) 141Ba 906(27) 620(40) JEFF 3.1.1 91Rb 2708(76) 2335(33) 142Ba 1059(64) 760(80) 91Rb∗ 2669(95) 2335(33) 143Ba 1343(49) 870(100) 0.2

Decay Heat (EEM) in MeV/fission −1 2 3 4 92Rb∗ 461(14) 393(32) 144Ba 785(33) 480(50) 10 1 10 10 10 10 93Rb 2523(53) 1920(100) 145Ba 1831(44) 1460(130) Time (s) 93Rb∗ 2397(25) 1920(100) 143La 424(9) 130(40) 94 ∗ +62 144 Rb 4063(−66) 4120(250) La 3158(68) 2240(230) Fig. 14. Impact of the inclusion of the total absorption mea- 93 145 Sr 2167(68) 1760(70) La 2144(52) 1480(80) surements performed for 13 decays in the gamma component 94Sr 1419(135) 1450(10) 145Ce 885(59) 770(70) of the decay heat calculations for 235U (see Figure 13 for more 95Sr 1790(43) 1180(100) 147Ce 1497(35) 620(10) 94Y 757(34) 900(50) 147Pr 929(32) 840(190) details).

0.8 0.6 0.7 0.6 0.5 0.5

0.4 0.4

0.3 239Pu Tobias 0.3 239 0.2 Pu Dickens et al. 239Pu Tobias JEFF 3.1.1 + TAGS 239Pu Dickens et al. 0.1 JEFF 3.1.1 0.2 JEFF 3.1.1 + TAGS JEFF 3.1.1 DecatHeat (ELP) in MeV/fission − 10 1 1 10 102 103 104

DecatHeat (EEM) in MeV/fission 0.1 Time (s) 10−1 1 10 102 103 104 Time (s) Fig. 15. Impact of the inclusion of the total absorption mea- surements performed for 13 decays in the beta component of Fig. 13. Impact of the inclusion of the total absorption the decay heat calculations for 239Pu (see Figure 13 for more measurements performed for 13 decays (86,87,88Br, 91,91,94Rb, details). 101Nb, 105Mo, 102,104,105,106,107Tc) published in Refs. [7,8,24, 62,67] in the gamma component of the decay heat calculations for 239Pu. 4 Neutrino applications

Nuclear reactors constitute an intense source of electron antineutrinos, with typically 1020 antineutrinos per sec- The results presented were provided by Dr. L. Giot [70]. In ond emitted by a 1GWe reactor. The reactor at Savannah the figures, it can be noted the large impact of the men- River was the site of the discovery of the neutrino in 1956 tioned decays and the relevance of the total absorption by Reines and Cowan [71], thus confirming Pauli’s pre- measurements for a proper assesment of the decay heat dictions of twenty-six years earlier [1]. Just like the decay based on summation calculations. heat described above, antineutrinos arise from the beta decays of the fission products in-core. Their energy spec- From the Figure 14, it is clear that additional mea- trum and flux depend on the distribution of the fission surements are needed for improving the description of the products which reflects the fuel content of a nuclear reac- 235U fuel, and new measurements are certainly required tor. This property combined with the fact that neutrinos for future fuels like the 233U/232Th case. are sensitive only to the weak interaction could make an- A. Algora et al.: Beta-decay studies for applied and basic nuclear physics 13

the Institute Laue-Langevin (ILL) in Grenoble (France) 1 by Schreckenbach and co-workers [77,78,79,80] with 235U, 239Pu and 241Pu thin targets under a thermal neutron 0.9 flux. These spectra exhibit rather small uncertainties and 0.8 remain a reference as no other comparable measurement has been performed since. Being integral measures, no in- 0.7 formation is available on the individual beta decay branches 0.6 of the fission products. This prevents the use of the conser- vation of energy to convert the beta into antineutrino spec- 0.5 tra. Schreckenbach et al. developed a conversion model, 0.4 235U Tobias in which they used 30 fictitious beta branches spread over 235 0.3 U Dickens the beta energy spectrum to convert their measurements JEFF 3.1.1 + TAGS into antineutrinos. In 2011 Mueller et al. [81] revisited the 0.2 JEFF 3.1.1 conversion method and improved it through the use of more realistic end-points and Z distributions of the fis- DecayHeat (ELP) in MeV/fission 0.1 − 10 1 1 10 102 103 104 sion products, available thanks to the wealth of nuclear Time (s) data accumulated over 30 years, and through the applica- tion of the corrections to the Fermi theory at branch level Fig. 16. Impact of the inclusion of the total absorption mea- in the calculation of the beta and antineutrino spectra. surements performed for 13 decays in the beta component of 235 After these revisions, the prediction of detected antineu- the decay heat calculations for U (see Figure 13 for more trino flux at reactors compared with the measurements details). made at existing short baseline neutrino experiments re- vealed a deficit of 3%. The result was confirmed immedi- ately by Huber [82] who carried out a similar calculation tineutrino detection a new reactor monitoring tool [72]. though he did not explicitly use beta branches from nu- Both particle and applied physics are the motivations of clear data. This antineutrino deficit was even increased their study at power or research reactors nowadays with by the revision of the neutron lifetime and the influence detectors of various sizes and designs placed at short or of the long-lived fission products recalculated at the time, long distances. In the last decade, three large neutrino ex- to finally amount to 6% [83]. A new neutrino anomaly was periments with near and far detectors, were installed at born: the reactor anomaly. Several research leads were fol- Pressurized Water Reactors [73,74,75], to try to pin down lowed since to explain this deficit. An exciting possibility the value of the θ13 mixing angle parameter governing is the oscillation of reactor antineutrinos into sterile neu- neutrino oscillations. These experiments have sought the trinos [83], which has triggered several new experimental disappearance of antineutrinos by comparing the flux and projects worldwide [84,85,86]. In 2015, the mystery deep- spectra measured at the two sites, both distances being ened when Daya Bay in China, Double Chooz in France carefully chosen to maximise the oscillation probability at and RENO in Korea, reported the detection of a distortion the far site. The three experiments [73,74,75] have now (colloquially called bump) in the measured antineutrino achieved a precise measurement of the θ13 mixing angle, energy spectrum with respect to the converted spectrum, paving the way for future experiments at reactors looking which could not be explained by any neutrino oscillation. at the neutrino mass hierarchy or for experiments at ac- The three experiments rely on the same detection tech- celerators for the determination of the delta phase, that nique and similar detector designs, which make it possible governs the violation of the CP symmetry in the leptonic that they would all suffer from the same detection bias as sector, thus shedding light on why there is an abundance suggested in [87]. But the three collaborations have thor- of matter rather than antimatter in the Universe. oughly investigated this hypothesis without success. In the Though they have used one or several near detectors face of the observed discrepancies between the converted in order to measure the initial flux and energy spectrum spectra and the measured reactor antineutrino spectra, of the emitted antineutrinos, the prediction of the latter it is worth considering more closely the existing methods quantities still enters in the systematic uncertainties of used to compute them and other possible explanations like their measurements, because their detectors are usually the case of nonlinear corrections discussed in Section 2 in not placed on the isoflux lines of the several reactors of relation to the 100Tc decay [42]. the plant at which they are installed [76]. In addition, the Double Chooz experiment started to take data with Converted spectra rely on the unique measurements the far detector alone, implying the need to compare the performed at the high flux ILL research reactor with the first data with a prediction of the antineutrino emission high resolution magnetic spectrometer BILL [88], using by the two reactors of the Chooz plant. Two methods thin actinide target foils exposed to a thermal neutron employed to calculate reactor antineutrino energy spectra flux that was well under control. This device was excep- were revisited at that time, i.e. the conversion and the tional as it allowed the measurement of electron spectra summation methods. ranging from 2 to 8 MeV in 50 keV bins (smoothed over The conversion method consists in converting the inte- 250 keV in the original publications) with an uncertainty gral electron spectra measured at the research reactor at dominated by the absolute normalization uncertainty of 14 A. Algora et al.: Beta-decay studies for applied and basic nuclear physics

3% at 90% C.L. except for the highest energy bins with tool to address these questions is to use the summation poor statistics [77,78,79,80]. The calibration of the spec- method. This method is based on the use of nuclear data trometer was performed with conversion electron sources combined in a sum of all the individual contributions of or (n,e−) reactions on targets of 207Pb, 197Au, 113Cd and the beta branches of the fission products, weighted by the using the beta decay of 116In providing calibration points amounts of the fissioning nuclei. Two types of datasets up to 7.37 MeV. The irradiation duration ranged from are thus involved in the calculation: fission product decay 12 hours to 2 days. Two measurements of the 235U elec- data, and fission yields. This method was originally de- tron spectrum were performed, the first one lasting 1.5 veloped by [95] followed by [96] and then by [46,97]. The days and the second one 12 hours. The normalisation of β/¯ν spectrum per fission of a fissile isotope Sk(E) can be the two spectra disagree because they were normalized broken down into the sum of all fission product β/¯ν spec- − 197 207 using two different (n,e ) reactions on Au and Pb tra weighted by their activity λiNi(t) similarly to what is respectively in chronological order. The measurement re- done for decay heat calculations: tained by the neutrino community is the second one. The X conversion procedure consists in successive fits of the elec- Sk(E) = λiNi(t) × Si(E) (5) tron total spectrum with beta branches starting with the i largest end-points. The total electron spectrum is fitted it- Eventually, the β/¯ν spectrum of one fission product eratively bin by bin starting with the highest energy bins, (S ) is the sum over the β branches (or beta transition and the contributions to the fitted bin are subtracted from i probabilities) of all β decay spectra (or associatedν ¯ spec- the total spectrum. The reformulation of the finite size tra), Sb (in equation 6), of the parent nucleus to the corrections, as well as a more realistic charge distribu- i daughter nucleus weighted by their respective beta branch- tion of the fission products and a much larger set of beta ing ratios according to: branches have been the key for the newly obtained con- verted antineutrino spectra of [81] and [82]. But the possi- Nb bility remains that the electron and/or converted spectra X b b b Si(E) = fi × Si (Zi,Ai,E0i,E) (6) suffer from unforeseen additional uncertainties. Indeed the b=1 normalisation of the electron spectra relies on the (n,e−) b reactions quoted above and on internal conversion coeffi- where fi represents the beta transition probability of the cient values that may have both been re-evaluated since b branch, Zi and Ai the atomic number and the mass b [89]. In addition, the exact position of the irradiation ex- number of the daughter nucleus respectively and E0i is periment in the reactor is not well known and may have the endpoint of the beta transition b. In 1989 the mea- an impact on the results as well [89]. Another concern surement of 111 beta spectra from fission products by is associated with the conversion model itself, where un- Tengblad et al. [46] was used for a new calculation of certainties may not take into account missing underlying the antineutrino energy spectra through the summation nuclear physics. In Mueller’s conversion model, forbidden method. But the overall agreement with the integral beta non-unique transitions are replaced by forbidden unique spectra measured by Hahn et al. [80] was at the level of transitions (when the spins and parities are known!). The 15-20% showing that a large amount of data were miss- shapes of the associated beta and antineutrino spectra are ing at that time. Lately, the summation calculations were not well known and the forbidden transitions dominate re-investigated using updated nuclear databases. Indeed the flux and the spectrum above 4 MeV. Several theoret- the summation method is the only one able to predict ical works have attempted to estimate the uncertainties antineutrino spectra for which no integral beta measure- introduced by this lack of knowledge [90,91,92]. The lat- ment has been performed. The existing aggregate beta est study [92] reports a potential effect compatible with spectra needed to apply the conversion method are rela- the observed shape and flux anomalies. Another source tively few and were measured under irradiation conditions of uncertainties comes from the weak magnetism correc- that are not exactly the same as those existing in power tion entering in the spectral calculation [82,93] that is not reactors. Among the discrepancies, the energy distribu- well constrained experimentally in the mass region of the tions of the neutrons generating the fissions in the ILL fission products. These two extra uncertainties affect con- experiments are different from those in actual power re- verted spectra and are not included in the published un- actors, and even more from the ones in innovative reactor certainties. Eventually the conversion process itself could designs such as fast breeder reactors. The aggregate beta be discussed, as the iterative fitting procedure is not the spectra were measured for finite irradiation times much only possible conversion method and it is suspected of in- shorter than the typical times encountered in power reac- ducing additional uncertainties [94]. tors. These few spectra and the specific conditions are not usable for innovative reactor fuels or require corrections In order to identify what could be at the origin of these for longer irradiation times (called off-equilibrium correc- anomalies, the understanding of the underlying nuclear tions) or more complex neutron energy distributions in- physics ingredients is mandatory. Indeed, only the decom- core. Until the recent measurement of the 238U beta spec- position of the reactor antineutrino spectra into their in- trum at Garching by [98], the conversion method could not dividual contributions and the study of the missing un- be applied to obtain a prediction of the 238U fast fission derlying nuclear physics will allow us to understand fully antineutrino spectrum. This was one of the motivations for the problem and provide reliable predictions. The best the first re-evaluation of the summation spectra that was A. Algora et al.: Beta-decay studies for applied and basic nuclear physics 15 performed in Mueller et al., the second being to provide Table 6. List of nuclides identified by the IAEA TAGS Con- off-equilibrium corrections [81] to the converted spectra. sultants that should be measured using the total absorption In this work, several important conclusions were already technique to improve the predictions of the reactor antineu- listed regarding summation calculations for antineutrinos. trino spectra. These nuclides are of relevance for conventional reactors based on 235U and 239Pu nuclear fuels. The list con- The evaluated nuclear databases do not contain enough tains 34 nuclides [103]. Relevance (Rel.) stands for the priority decay data to supply detailed beta decay properties for all of the measurement. Isotopes marked with asterisks show the the fission products stored in the fission yields databases. measurements performed by our collaboration, m stands for The evaluated databases have thus to be supplemented by metastable or isomeric state. other data or by model calculations for the most exotic nu- Isotope Rel. Isotope Rel. Isotope Rel. clei. The relative ratio of the aggregate beta spectra with ∗ the obtained summation spectra from databases exhibited 36-Kr-91 2 39-Y-97m 1 53-I-138 2 a shape typical of the Pandemonium effect, with an overes- 37-Rb-88 1 39-Y-98m 1 54-Xe-139 1 37-Rb-90 1 39-Y-99∗ 1 54-Xe-141 2 timate of the high energy part of the spectra in the nuclear ∗ data. The maximum amount of data free of the Pande- 37-Rb-92 1 40-Zr-101 1 55-Cs-139 1 37-Rb-93∗ 1 41-Nb-98∗ 1 55-Cs-140∗ 1 monium effect should thus be included in the summation ∗ ∗ calculations. The difficulty comes from the fact that these 37-Rb-94 2 41-Nb-100 1 55-Cs-141 2 38-Sr-95∗ 1 41-Nb-101∗ 1 55-Cs-142∗ 1 Pandemonium-free data are usually not included in the 38-Sr-96 1 41-Nb-102∗ 1 57-La-146 2 evaluated databases. One has thus to gather the exist- 38-Sr-97 2 41-Nb-104m 2 ing decay data and compute the associated antineutrino 39-Y-94 1 52-Te-135 1 spectra. The Pandemonium-free data are mostly existing 39-Y-95∗ 1 53-I-136 2 TAGS measurements [17] and the electron spectra directly 39-Y-96∗ 1 53-I-136m 1 measured by Tengblad et al. [46]. They were included in 39-Y-97 2 53-I-137∗ 1 an updated summation calculation performed in [99], in which the seven isotopes measured with the TAGS tech- nique that had so much impact on the 239Pu electromag- netic decay heat, i.e. 105Mo, 102,104−107Tc, and 101Nb [7], surements performed by our collaboration marked with were taken into account. The calculation revealed that asterisks. More than half of the first priority nuclei have these TAGS results had a very large impact on the cal- been measured by our collaboration with the TAGS tech- culated antineutrino energy spectra, reaching 8% in the nique. The Oak Ridge group is involved in similar studies, Pu isotopes at 6 MeV. But it appeared that summation see for example the results for several isotopes published calculations still overestimate the beta spectra at high en- in [101,102]. ergy, indicating that there were large contributions from In 2009, 91−94Rb and 86−88Br were measured with the nuclei where the data suffer from the Pandemonium ef- Rocinante TAGS (for details see [24,62] and Figure 9) fect in the decay databases. The situation is thus similar placed after the JYFLTRAP Penning trap of the IGISOL to that already encountered in the decay heat summation facility [51]. Only 92,93Rb were in the top ten of the nu- calculations. These conclusions reinforced the necessity for clei contributing significantly to the reactor antineutrino new experimental TAGS campaigns and spread the mes- spectrum. 92Rb itself contributes 16% of the antineutrino sage worldwide. New summation calculations were devel- spectrum emitted by a pressurized water reactor (PWR) oped and other experimental campaigns were launched us- between 5 and 8 MeV. Its contributions to the 235U and ing the TAGS technique [100,101,102]. In [100] a careful 239Pu antineutrino spectra are 32% and 25.7% in the 6 to study of the existing evaluated fission yield databases was 7 MeV bin and 34 and 33% in the 7 to 8 MeV bin. In 2009, performed. It appeared that the choice of the fission yield the ground state (GS) to GS beta intensity of this decay database had a large impact on the summation spectra was set to 56% in ENSDF. This value was revised in 2014 obtained, because of mistakes identified in the ENDF/B- to 95.2%. A maximum of 87%±2.5% was deduced from VII.1 fission yields for which corrections were proposed. our TAGS data, having a large impact on the antineutrino Once corrected, the ENDF/B-VII.1 fission yields provide spectra [67]. This value was confirmed by the Oak Ridge spectral shapes in close agreement with the JEFF3.1 fis- measurements [101]. The 92Rb case is worth noting be- sion yields. In 2012, the agreement obtained was at the cause it is not a case suffering from Pandemonium, but its level of 10% with respect to the integral beta spectra GS to GS beta branch was underestimated in former eval- measured at ILL and the number of nuclei requiring new uations. In the analysis of this nucleus, the sensitivity of TAGS measurements was considered as achievable. Lists the reconstructed spectrum (and thus of the χ2 obtained of priority for new TAGS measurements were established ) to the value of the GS-GS branch was very high, because first by the Nantes group [67] (which triggered our first of the large penetration of the electrons in the TAGS. The experimental campaign devoted to reactor antineutrinos quoted uncertainties were obtained by varying the input in 2009), then by the BNL team [100] and eventually a ta- parameters entering into the analysis, such as the calibra- ble based on the Nantes summation method was published tion parameters, the thickness of the beta detector, the in the frame of TAGS consultant meetings organized by level density, the normalisation of the backgrounds, etc.. the Nuclear Data Section of the IAEA [103]. A portion of The beta decay data for 92Rb that were used in the pre- the table from [103] is shown in Table 6, with the mea- vious summation calculations [99] were those from Teng- 16 A. Algora et al.: Beta-decay studies for applied and basic nuclear physics blad et al. The impact of replacing these data with the 235 1.04 1.04 new TAGS results amounts to 4.5% for U, 3.5% for 239 241 239Pu, 2% for 241Pu, and 1.5% for 238U. A similar impact 1.02 Pu1.02 Pu was found on the summation model developed by Son- 1 1 zogni et al. [100] but a much larger impact (more than 25% in 235U) was found on another model in which no 0.98 0.98 Ratio (w/wo new data) Pandemonium-free data were included [104]. 0.96 0.96 86−88 Though not motivated by neutrino physics, Br 0.94 0.94 and 91,94Rb were measured in the same experiment. 86−88Br 91 0.92 0.92 and Rb were not in the priority list of [103]. The main 1.04 1 2 3 4 5 6 71.04 8 1 2 3 4 5 6 7 8 motivation for those cases was the study of moderate beta 238U 235U delayed neutron emitters using complementary techniques 1.02 1.02 and the study of the decay used as normalization in the 1 1 measurements by Rudstam et al [45] already mentioned 0.98 0.98 in Section 3. These TAGS measurements confirmed the Ratio TAGS2017 / TAGS2012 Pandemonium problem in the existing data. 86,87Br and 0.96 0.96 91Rb did not show a large impact on the antineutrino spec- Ratio TAGS2017 / Greenwood 0.94 0.94 tra [12,24,62]. On the other hand, 94Rb, ranked as priority 2 in the table from [103], and 88Br exhibited a quite large 0.92 0.92 impact on the spectra. This was verified with two different 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 Energy (MeV) Energy (MeV) summation calculations [24]. In one of the models, the new Energy (MeV) TAGS data replaced high resolution spectroscopy data, Fig. 17. Accumulated impact of the beta intensities of the and thus the observed impact was typical of a correction 86,87,88Br and 91,92,94Rb [24,62,67] decays measured with the of the Pandemonium effect i.e. a decrease of the high en- total absorption spectrometer Rocinante on the antineutrino ergy part of the aggregate antineutrino energy spectrum. spectra with respect to that published in [99] (relative ratios) The impact reached 4% in 235U and 239Pu in the case of for the thermal fissions of 235U, 239Pu and 241Pu, and the fast 94Rb and was more modest as regards 88Br with a 2-3% fission of 238U [107]. decrease in the latter actinides between 8 and 9 MeV. The latter range explains the reason why 88Br did not belong to the priority list of [103] that was established for a con- Nb is a refractory element and the isomers in 100Nb and tribution to the PWR antineutrino spectrum larger than 102Nb are separated by only 313 keV and 94 keV respec- 1% between 3 and 8 MeV. In the second model the TAGS tively. The half-lives are very similar 1.5 s and 2.99 s in data replaced data measured by Tengblad et al. that were 100Nb and 4.3 s and 1.3 s in 102Nb for the ground and considered in the model because they were assumed to 100 102 87 isomeric states respectively. Nb and Nb have been be Pandemonium-free. The replacement of Br had little assigned a top priority in the list of [103]. 100Nb is among impact, that of 94Rb led to a 3% decrease at 8 MeV but 88 the main contributors to the antineutrino flux in the re- that of Br brought a 7% increase between 8 and 9 MeV, gion of the shape distortion, along with 92Rb, 96Y and with a cancellation of the last two effects below 8 MeV. 142Cs. The results showed that the high resolution mea- The cumulative impact of the TAGS beta intensities surements for 100,100mNb and 102gsNb were affected by the measured with the Rocinante detector at Jyv¨askyl¨aon the Pandemonium effect, while the beta-intensity distribution antineutrino energy spectra generated after the thermal for 102mNb was determined for the first time [13]. The fissions of 235U, 239Pu and 241Pu, and fast fission of 238U impact of these measurements on the summation calcu- are presented in Figure 17 with respect to that built with lations was evaluated (see Figure 18) and resulted in a the most recent evaluation decay databases JEFF3.3 [105] large impact between 3 and 7 MeV, with a strong decrease and ENDF/B-VIII.0 [106] for the same nuclei and con- of the spectrum peaked at 4.5 MeV and a strong increase taining only the TAGS data from [7,17]. The decrease of peaked at 6.5 MeV, in the region of the shape distortion. the two plutonium spectra above 1.5 MeV is remarkable, In the calculation, the TAGS data replaced high resolu- reaching 8%. The impact on the two uranium isotopes tion spectroscopy data extracted from JEFF3.3 [105] and amounts to about 2% and 3.8% in the 3 to 4 MeV range ENDF/B-VIII.0 [106]. As a result, the discrepancy be- in 235U and 238U respectively. These results were provided tween the summation antineutrino spectra including these by Dr. M. Estienne [107]. data and the experimental reactor antineutrino spectra is In our 2014 experimental campaign, we were almost diminished in the region of the shape distortion, though exclusively focussed on nuclei of importance for the pre- the distortion has not vanished completely [13]. The re- diction of the reactor antineutrino spectrum and for decay sults presented in this last figure were also provided by heat calculations using the DTAS detector [30]. Twenty- Dr. M. Estienne [107]. three isotopes were measured, among them many isomers In parallel to the TAGS campaigns, the reactor an- which require the separation power of the Jyv¨askyl¨aPen- tineutrino experiments have published their near detector ning trap. An illustration of the experimental challenge is measurement of the emitted antineutrino flux and spec- given by the case of the Niobium isomers 100,100m,102,102mNb. trum from PWRs. In 2017, the Daya Bay experiment A. Algora et al.: Beta-decay studies for applied and basic nuclear physics 17

1.06 1.06 1.1 239Pu 241Pu 1.04 1.04 1 0.9 1.02 1.02 DB/SM•2018 0.8 DB/SM•2017

1 1 Ratio DB/H.M.(SM) DB/H.M. 1.1 2 3 4 5 6 7 8 0.98 0.98 1 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 SM•2018/H.M. 1.06 1.06 0.9 238U 235U SM•2017/H.M. Ratio SM/H.M. 1.04 1.04 2 3 4 5 6 7 8 Energy (MeV) Energy (MeV) 1.02 Ratio TAGS2018 / TAGS2017 1.02 Fig. 19. Comparison of the summation antineutrino spec- trum obtained using the fission fractions published in [113] 1 1 and all the TAGS data quoted in this section, with the exper- 0.98 0.98 imental spectrum from reference [113]. Ratios to the Huber- Mueller (H.M.) model are also provided for comparison. SM- 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 year stands for summation model using the TAGS data an- EnergyEnergy (MeV) (MeV) Energy (MeV) alyzed until the given year (see also Figure 20 for additional details). Reprinted figure with permission from [110], Copy- Fig. 18. Accumulated impact of the beta intensities measured right (2019) by the American Physical Society. with the DTAS detector on the antineutrino spectra with re- spect to that presented in Figure 17 (relative ratios) for the × −42 thermal fissions of 235U, 239Pu and 241Pu, and the fast fission 10 of 238U [107]. The figure represents the relative impact of the 0.63 100,100m,102,102mNb decays [13]. Greenwood /fission] 0.62 2

[cm 0.61 f could measure the reactor antineutrino flux associated σ SM•2012 0.6 SM•2015 with various fuel compositions [108], and found a flux SM•2017 239 SM•2018 coming from Pu fission in agreement with the predic- 0.59 GW tion of the Huber-Mueller model, while the flux associated SM•2012 235 0.58 SM•2015 with U fission exhibited a deficit of 7% thus nearly ex- SM•2017 plaining by itself the reactor anomaly. This new result SM•2018 0.57 DB does not favour the idea of oscillation into sterile neutri- nos, as it would affect equally the antineutrinos arising 0.24 0.26 0.28 0.3 0.32 0.34 0.36 F from both fuels. It would rather confirm the hypothesis of 239 an additional systematic uncertainty associated with the 235 Fig. 20. Comparison of the Inverse Beta Decay (IBD) yield U energy spectrum. These recent findings reinforced computed with the summation antineutrino spectrum obtained the necessity of an alternative approach to the converted using the fission fractions published in [108] for 239Pu and us- spectra which could be brought by the use of nuclear ing all the TAGS data quoted in this section (included succes- data. It was thus timely to perform a comparison of the sively), with the experimental IBD yield from [108]. Greenwood summation method spectra with the Daya Bay results. represents the result of the summation model [110] when only The first comparison was performed in [109] showing a the TAGS results of Greenwood et al. [17] are included (for discrepancy with the measured antineutrino flux of only more details of the model see [110]). SM-2012 represents the 3.5%, nearly twice as small as that with the Huber-Mueller additional impact of the TAGS measurements published in [7] model. We have performed an update of our summation (102,104,105,106,107Tc, 101Nb and 105Mo). SM-2015 contains in model in [110] using the above-mentioned Pandemonium- addition the effect of 92Rb [67]. SM-2017 represents the impact free datasets improved by the TAGS campaigns of the last of 86,87,88Br and 91,94Rb decays [24,62], and SM-2018 contains 100,100m,102,102 decade, the most recent evaluated databases (JEFF3.3, the impact of Nb decays [13] (always considered ENDF/B-VIII.0) and updated gross theory spectra [111] in addition to the earlier version of the summation model). for the unknown beta decay properties. Reprinted figure with permission from [110], Copyright (2019) by the American Physical Society. After folding with the Inverse Beta Decay (IBD) cross section [112] the summation spectrum built with the ac- tinides spectra weighted with the fission fractions pub- lished by Daya Bay, the resulting detected spectrum was compared with that of Daya Bay [113] and that built us- ing the Huber-Mueller model. In Figure 19, the top panel 18 A. Algora et al.: Beta-decay studies for applied and basic nuclear physics shows the ratio of the Daya Bay antineutrino spectrum anomaly arises solely from 235U. It is worth mentioning over that computed with the Huber-Mueller model (open also that PROSPECT is the first detector using 6Li in- diamonds with error bars) superposed with the ratio of stead of Gd to capture the neutron formed in the IBD Daya Bay over the summation method spectrum includ- process since the Bugey experiment [115], which did not ing the TAGS results from our first campaign (dashed line) see a shape anomaly either. Lately Double Chooz has also and over the summation method spectrum including the released their fourth measurement of the θ13 mixing angle TAGS results from both campaigns (plain line). The nor- obtained by cumulating neutron captures on Gd and the H malisation of the summation method spectrum is clearly in and C contained in the target and gamma catcher volumes better agreement with the experimental data than that of [116]. They observe a shape distortion which could be fit- the Huber-Mueller spectrum (closser to 1), which is con- ted either with a single or a double Gaussian with a slope. sidered nowadays the model reference. The inclusion of One of their conclusions is that the one sigma envelope the TAGS measurements of the Niobium isomers [13] has for today’s prediction appears insufficient to accommo- further improved the shape agreement especially in the date the mismatch between data and model for both rate energy region of the shape distortion. The bottom panel and shape. A better understanding of the origin of model of Fig. 19 shows the ratio of the summation method spec- deviations remains critical and the role of nuclear data is trum with that of Huber-Mueller. Here again the latest definitely crucial at the time at which experiments are be- TAGS measurements have flattened the ratio which shows ing set up to measure the mass hierarchy of neutrinos. In a rather good shape agreement, though located below one a recent publication [117], the global reactor antineutrino at about 95-96%. Still the summation method spectrum data set was re-analyzed using three reactor antineutrino does not reproduce the shape distortion seen by the reac- flux predictions, the Huber-Mueller model, the summa- tor antineutrino experiments at PWRs. Figure 20 summa- tion method of [110] and the model of [92] which includes rizes the detected antineutrino flux (called IBD yield) as a a theoretical calculation of the form factors for the first function of the fission fraction of 239Pu obtained with the forbidden transitions. Relative to the traditional Huber- summation method spectra depending on the TAGS re- Mueller predictions, the two new calculations result in di- sults included in the calculation. The explicit labels of the verging evidence for a sterile neutrino when total IBD rate lines describe the TAGS results introduced one after the measurements are considered. The summation calculation other. It is noticable that the inclusion of more TAGS data of [110] decreases the significance from 2.3 to 0.95 σ, while systematically decrease the detected antineutrino flux to that of [92] increases the significance to 2.8 σ. However, end with an 1.9% discrepancy with the Daya Bay mea- the spectral anomaly is robust with any of the flux models. sured IBD yield. This is a consequence of the correction The accurate determination of the reactor antineutrino of the Pandemonium effect in nuclear databases and em- spectra is also mandatory to monitor future reactors with phasizes the importance of the TAGS method and mea- antineutrino detection. Predictions for innovative reactor surements. More details are given in [110] in which the designs and fuels can only be obtained through the use of individual IBD yields associated with 235U, 239Pu, 241Pu, nuclear data and the summation method. The fine struc- and 238U obtained with the summation model are also tures present in the antineutrino energy spectra induced compared with the Daya Bay results. The agreement is by the end-points of the individual beta branches from the good in general for all four isotopes. This is at variance fission products [104,118] could provide a benchmark for with the Huber-Mueller model for which a large discrep- nuclear data and an insight of what is going on inside a ancy is observed in the case of 235U while the three other reactor. But they also degrade the sensitivity of detectors cases are in very good agreement with the experiment. such as JUNO [119] by mimicking a periodic oscillation pattern. These fine structures may be directly observed In our 2014 TAGS campaign at Jyv¨askyl¨adevoted to by the JUNO-TAO one-ton detector that will be located reactor antineutrinos and decay heat, 96,96mY, 140,142Cs, a few metres away from a PWR core [120]. In parallel, 138I, 137I, 95Rb, 95Sr, 103Mo and 103Tc were measured as an experimental confirmation of the observed first hint well. These future TAGS results may complete the pic- of coherent elastic neutrino-nucleus scattering [121] would ture that starts to be drawn of the reactor antineutrino definitely open new possibilities for neutrino applications. energy spectra. In parallel to the nuclear physics effort, reactor antineutrino experiments at short baseline from research reactors start to release their first results. Up 5 Nuclear structure to now, only the NEOS and Neutrino-4 collaborations have released a combined result which signals the pres- In an article about the application of TAGS, it would be ence of an oscillation [114]. Neither the STEREO [85] remiss of us to neglect its application to the study of nu- or the PROSPECT [86] experimental results confirm this clear structure. It is not our intention here to tell the oscillation signal. Furthermore, the PROSPECT experi- reader all about beta decay. That can be found in text ment has released their first spectral measurement of the books (see for example [122,123,124,125]). Instead what antineutrino energy spectrum from Highly Enriched Fuel we want to do is provide a few examples that show how (HEU) which is equivalent to a pure spectrum from 235U. useful TAGS can be in testing nuclear models that con- It is remarkable that their shape-only result does not show tribute to our understanding of the underlying structure such a pronounced shape distortion as the large experi- of the atomic nucleus, and in particular present some cases ments at PWRs. It thus excludes the idea that the shape recently studied in the framework of reactor applications. A. Algora et al.: Beta-decay studies for applied and basic nuclear physics 19

In Section 2 we already mentioned the 100Tc case, the case of GT transitions, is normally concentrated in a of relevance for double beta decay studies. Here we will resonance at relatively high excitation energy, for exam- focus on two nuclear structure applications of TAGS that ple in the range of 8-15 MeV for A∼100, that is difficult are of significance, namely the study of of the quenching of to access in beta decay. In consequence, charge-exchange Gamow-Teller transitions and the study of nuclear shapes. reactions with hadronic probes, such as (p,n), (3He,t) or One essential concept in beta decay, important in the (t,3He), have been used to measure the full strength. Ex- examples that follow, is the beta strength function (see tracting the GT strength from these probes is more com- [14]), a quantity that can be deduced from experiment. It plicated than extracting it from beta decay. Among other is defined as: reasons, this is because it relates to the penetrability of the hadronic probe in the nucleus and because of the dif- Iβ(E) ficulty of selecting the GT process in a clean way. Beta Sβ(E) = (7) f(Qβ − E)T1/2 decay, however, has its own difficulties. The principal one, as mentioned above, is to know how much of the strength where Iβ(E) is the beta intensity to the level at exci- lies within the Q-value window, and the other difficulty is tation E in the daughter nucleus, f is the statistical rate to be sure that we measure all the strength inside the Qβ Fermi integral which depends on the energy available in window, because of the Pandemonium effect. It is in over- the decay (Qβ − E) and T1/2 is the half-life of the decay. coming this second difficulty that the TAGS technique has Sβ(E) is in practical terms the reciprocal of the ft values had an impact in tackling this problem. given conventionally in the literature. We will concentrate on our contribution to the determination of the strength by measuring the beta feeding in a reliable way, which is In order to avoid the first problem, one can choose the main subject of this article. The other two quantities, cases where most of the strength is expected to be located namely Qβ − E or the T1/2 are obtained from measure- at relatively low energy, inside the Qβ window, and this ments dedicated to this purpose. In the following we will happens, in principle, in the beta decay of nuclei south east focus on allowed Gamow Teller transitions, since allowed of 100Sn on the Nuclear Chart and in the rare-earth nuclei Fermi transitions are normally concentrated in a single above the spherical nucleus 146Gd. These cases, even al- state, and not affected by P andemonium very much. The though they do not have a direct relation with the cases of experimental beta strength is related to the experimental relevance for reactor applications presented in this article, B(GT) in the case of Gamow Teller transitions through can provide information on the necessary corrections that the following equation: are required for a proper theoretical description of the beta decay process. The reason, in both the 100Sn and above 1 gA 2 X exp 146Gd regions, is that there is only one main component in Sβ(E) = ( ) B(GT )i→f (8) 6147 gV + E the GT strength on the β side, namely πg9/2→νg7/2 in the 100Sn region and πh →νh in the rare-earth case. where g and g are the axial-vector and vector cou- 11/2 9/2 A V All other proton occupied orbitals have no empty neutron pling constants. The B(GT ) as defined above can be re- orbital partner. Unfortunately, the expected B(GT) can- lated to the transition probability calculated theoretically not be directly compared with the Ikeda sum rule in these between the parent state and the states populated in the cases because this rule involves the B(GT) values for both daughter defined as follows: the β+ and the β− decays and here only the former can X X be measured. So, it has to be compared with theory. A B(GT )theo = | hΨ | σµ t± |Ψ i |2 (9) i→f f k k i relatively simple but realistic calculation of the expected µ k beta strength on the β+ side was carried out by Towner where σ and t represent the spin and isospin operators [129] for decays in both of these regions of the Segre Chart. acting on the individual nucleons and Ψi and Ψf the initial In this work [129] a hindrance factor h is defined as the and final nuclear states. ratio between the summed GT strength from theory and In consequence, a comparison of the B(GT )theo should experiment. Initially he adopted the extreme single parti- reproduce the B(GT ) determined in the experiment. Ac- cle approach (s.p), namely considering only the two pairs tually, the quality of the comparison reflects the good- of orbitals, πg9/2-νg7/2 and πh11/2-νh9/2. He then made ness of the nuclear model in describing the involved nu- a series of corrections to this approach taking into ac- clear states. In addition there is a model independent rule, count pairing, core polarization and higher-order effects called the Ikeda sum rule, that tells us how much strength and then looked at how hindered the corrected theoretical we should observe. Curiously enough, the strength ob- strength would be in comparison with the extreme s.p pic- tained experimentally seems to be systematically lower ture. This result defines a theoretical hindrance factor that than theory. This is called the Gamow Teller quenching can be compared later with the hindrance obtained from problem and it has been discussed for more than four the ratio of the extreme single particle approximation and decades and is not yet fully resolved (see for instance [126, experiment. The theoretical hindrance was calculated for 127] and more recently [128] and references therein). The the range of cases from n=1 to n=10 active protons in the 100 discussion of this mismatch between theory and exper- g9/2 orbital in the Sn region and n=1 to n=12 in the iment involves theoretical as well as experimental argu- h11/2 orbital in the rare earths. ments. One main difficulty is that the full strength, in 20 A. Algora et al.: Beta-decay studies for applied and basic nuclear physics

A series of experiments were carried out at GSI (Ger- importance of the TAGS experiments and the limitations many) with heavy ion beams from the UNILAC at ener- of the Ge detectors in terms of observing beta feeding at gies slightly above the Coulomb barrier on the appropriate high excitation energy that was discussed in the intro- targets to study relevant beta decays in these regions of duction. We see the B(GT) distribution measured with interest. At these energies, the reaction was dominated by the Cluster cube [135] and with the GSI TAS [136]. The the fusion evaporation channels which are fewer than in Cluster cube was an array of six Euroball Ge cluster detec- the fission examples described in previous sections. Con- tors in compact geometry. It was equivalent to forty two sequently, the separation achieved with the relatively sim- individual Ge detectors and had an efficiency of 10.2(5) ple Mass SEParator (MSEP) [130], provides clean enough % at a gamma-ray energy of 1332 keV. The figure shows samples to perform the experiments. The GSI TAS [131] clearly the importance of both types of measurement. In was built and briefly used at the Berkeley SuperHILAC the Ge measurements 1064 gamma rays were identified and after the accelerator was closed, it was installed at and the coincidences between detectors allowed the con- the GSI MSEP. This spectrometer enjoyed two advan- struction of a decay scheme with 295 levels in 150Dy [135]. tages over the INEL Idaho TAGS [65]. Firstly, the crys- Figure 21 shows in blue the B(GT) strength to each of tal was more than twice the size, secondly it included a these levels as deduced from the beta feedings in the de- small cooled high purity Ge detector for X-Ray detection. cay scheme. Inspection of the total absorption spectrum The first improvement was important for a better response reveals that the Ge array loses sensitivity as a function of of the spectrometer to the absorption of the gamma cas- excitation energy in the daughter nucleus when compared cades, and the second to clean the EC (Electron Capture) with the TAGS and our ability to determine the feed- component of the decays further and hence to obtain a ing or beta intensity distribution diminishes. Once con- very good Z separation. The results can be seen in refer- verted into B(GT) strength we conclude that we lose 50% ences [132] (100In), [133] (97Ag), [134] (148Dy) [135, of the total strength compared with the TAGS measure- 136] (150Ho) and [137] (148Tb(2− and 9+ isomers), and ment. Moreover, the tail of the resonance, one of the foci 152Tm(2− and 9+ isomers)). For the very special case of of interest in the experiments discussed above cannot be 100Sn, where the expectations are that all the strength seen with the Ge detector array. is concentrated in a a single 1+ state in the daughter, we will consider the results of Hinke et al. [138] and the more In summary, returning to the discussion of the miss- recent work by Lubos et al. [139] measured with Ge de- ing B(GT) strength in beta decay, even though the ex- tectors. To study this case further, a TAGS experiment periments explained above are probably the best cases to has been proposed and partially carried out at RIKEN study the Gamow Teller quenching, they rely very much [140] and is currently under analysis [141]. In general, one on comparison with theoretical calculations which, in gen- observes that the calculations [129] reproduce the ob- eral, cannot locate with sufficient precision whether the served hindrance factor fairly well for the 100Sn region. calculated strength is inside the accessible beta window One should mention here that this case is simple enough or not. However, these measurements have demonstrated that it has been calculated from first principles reproduc- that the tail below the Gamow Teller resonance exists, and ing the experimental value also fairly well [128]. At the this observation is free of background ambiguities. More- time of this last work [128] only the [138] results were over, in the future, when either the calculations are accu- available and included in the comparison, but the more rate enough to tell us how much of the strength should recent results of [139] show even better agreement with be located within the accessible beta-window, or, alter- these calculations, similar in quality to the agreement with natively when we are able to perform charge exchange the systematic extrapolation of the strength from [142]. In reactions using radioactive beams, we have here very reli- contrast, in the rare-earth region higher hindrance factors able measurements of that part of the spectrum that lies have been observed experimentally compared to Towner’s below the Q energy. This can be used for normalisation calculations. One should note that, somewhat surprisingly, β purposes as well as for control of the reaction mechanism. the GT resonance is clearly observed in this case. More- over, the tail below the resonance that has been observed experimentally and discussed at length in the Charge Ex- Another application of TAGS measurements, first pi- change reaction experiments, is clearly seen in these beta oneered at CERN-ISOLDE with the Lucrecia TAGS, re- decay experiments for the first time. As an example, we lates to the shapes of nuclear ground states. The concept show in Figure 21 the case of the decay of the 150Ho 2− of nuclear shape is deceptively simple. In practice it is isomer to 150Dy [135], with the TAGS measurement rep- difficult to measure. The measurements with TAGS are resented by the spectrum under the black line. A similar based on a theoretical idea put forward by Hamamoto and result was obtained in the 152Tm case reported in [137]. Zhang [143], that was developed further by Sarriguren et In this article, it was suggested that the missing strength, al. [144] and Petrovici et al. [145]. They showed that the or in other words the explanation of the disagreement with beta strength distribution for transitions to excited states Towner, is probably located in that part of the tail of the in the daughter nucleus depends on the shape assumed for resonance which is cut off by the Qβ window. the ground state of the decaying nucleus. Intuitively one can see why this might be so if we look at the ordering of The same Figure 21 can also be used to illustrate the deformed single particle orbits on a Nilsson diagram. The levels on the prolate and oblate sides are in different order A. Algora et al.: Beta-decay studies for applied and basic nuclear physics 21

0 2 4 6(MeV) 8 ] π 103 103 ) 0.5 Mo → Tc /4 0.3 -1 2 A DTAS 0.4 β-strength 0.25 keV Oblate -1 150Ho(2-) 150Dy s 0.2 0.3 B(GT) [g

-6 Prolate

Σ 0.15 0.2 0.1 FWHM=240 keV 0.1 0.05 EC Q 0

-strength (10 0 0 500 1000 1500 2000 2500 3000 β 100 200 300 400 Energy [keV] channel (bin=20 keV) Fig. 22. Comparison of the deduced beta strength for the Fig. 21. Comparison of the beta strength deduced from the 103 150 − decay of Mo [40,147] in comparison with QRPA calculations high resolution measurement of the beta decay of the Ho 2 assuming prolate or oblate deformations in the ground state of isomer using the cluster cube setup [135] (shown in blue) with 103 gA Mo [148]. In the model a quenching factor of ( )eff = the strength obtained from a total absorption measurement gV 0.77( gA ) is applied. [136] (black) . The measurements were performed at the Mass gV Separator at GSI. Reprinted figure with permission from [135], Copyright (2003) by the American Physical Society. was obtained assuming a ground state deformation of 2=- 0.31 for 105Mo. The experimental half-life of this decay is and thus filling them up to the Fermi level to determine 35.6 s, and this value can be better reproduced if first for- the ground state configuration of a particular nucleus in- bidden transitions are included in the model calculation theo volves different single particle contributions. Their beta (T1/2 =30.3 s), but in that case, the experimental beta decay strength distributions will also be different since distribution is not reproduced so well. This can be seen they are dictated by angular momentum and parity selec- in Figure 23 where the experimental feeding distribution tion rules as well as the overlap of the wavefunctions of is compared with the theoretically deduced distributions the states involved. The calculations by Hamamoto and with and without first forbidden transitions. A better re- Zhang, Sarriguren et al. and Petrovici et al., are of course production of the beta distribution by theory is obtained rather more sophisticated than this simple picture which if no first forbidden component is included in the model. is just used for understanding the underlying physics phe- But in that case the experimental half-life is not so nicely theo nomena. reproduced (T1/2 =150 s). This clearly shows a limitation In particular regions of the nuclide chart, nuclei can of the performance of this model in a region which is dom- have several minima in the potential energy surface with inated by shape effects and where triaxiality can play a different shapes for the ground state. The calculated B(GT) role. QRPA calculations assume that both the parent and distributions for each of these states with a defined defor- the daughter have the same deformation, which might not mation are quite different in some but not all cases (see always be applicable in regions where shape transitions for example [144]). Where they are different, the experi- are common. This example shows the relevance of having mental B(GT) distribution measured with TAGS can then in addition to the experimental half-life the possibility of be compared with the theoretical distributions and the comparing the theoretical strength (or the deduced theo- ground state shape inferred. A number of studies of this retical feeding) with reliable experimental data, like that kind ([5], [6], [9], [10], [11]), have been carried out for nu- provided by TAGS measurements. Based on the descrip- clei with A∼ 80 and A∼190. A summary of these activities tion of the half-life only, we might conclude it is nece- at ISOLDE can be found in [16]. sary to introduce the first forbidden component for the This method has also been applied for some of the description of this decay, which does not reproduce well cases studied at IGISOL. See for example 100,102Zr and the experimental beta feeding. The relevance of this kind 103Mo [40,146]. In Figure 22 [40,147] we present a compar- of model validation will be further discussed in the next ison of the deduced strength for the decay of 103Mo with Section in relation to astrophysical applications. Quasiparticle Random Phase Approximation (QRPA) cal- culations performed by P. Sarriguren [148]. From this com- parison a preference for an oblate shape in the ground 6 Astrophysical applications state of 103Mo can be inferred. In the calculations a quench- gA gA ing factor of ( )eff = 0.77( ) has been applied, which gV gV TAGS measurements are important also in the context is equivalent to a hindrance factor of 1.69 with respect to of nuclear astrophysics. We select here some examples the QRPA calculations used in the comparison. related to the astrophysical r process. As mentioned in Another example of the importance of TAGS measure- the previous Section, some of those examples will show a ments in testing models is provided by 105Mo. The decay strong interrelation with nuclear structure studies. of 105Mo was calculated using the FRDM-QRPA model The r process is driven by a huge instantaneous flux [149,150]. The best theoretical description of this decay of neutrons that creates by successive neutron captures 22 A. Algora et al.: Beta-decay studies for applied and basic nuclear physics

aration energy (Sn) becomes smaller than the decay Qβ 40 : TAGS feeding value and neutron emission from populated neutron un- [%] β

I : theoretical feeding bound states occurs. In spite of current efforts at the most advanced radioactive beam facilities to determine this in- 30 formation experimentally [153], most of the nuclei involved cannot be accessed in the laboratory and need theoreti- cal estimates. The key point here is that both quantities 20 are derived from the beta strength distribution Sβ(E) (see also Equation 7) 10 1 Z Qβ = Sβ(E)f(Qβ − E)dE (10) 0 T1/2 0 0 1 2 3 4 5 Q Z β Γ E [MeV] P = T n S (E)f(Q − E)dE (11) x n 1/2 Γ + Γ β β 40 : TAGS feeding Sn n γ [%] β

I : theoretical feeding Equation 11 above includes the competition between 30 neutron (Γn) and gamma (Γγ ) emission. It should be noted that models often assume that neutron emission prevails always and the competition is ignored. 20 The quality of beta strength calculations is usually as- serted by global comparisons with measured half-lives and to a lesser extent with measured neutron emission proba- 10 bilities. However it is found that different theoretical mod- els with comparable quality predict quite different T1/2 and Pn (see for example [154]). This clearly indicates that 0 0 1 2 3 4 5 the quality assessment based on these integral quantities (Equations 10 and 11) is not good enough. This comes Ex [MeV] as no surprise since several (theoretical) strength distri- Fig. 23. Comparison of the experimentally deduced beta feed- butions can lead to the same half-life for a particular nu- ing in the decay of 105Mo with the results of theoretical cal- cleus. But the underlying nuclear structure can then pre- culations using the FRDM-QRPA model [149,150]. The upper dict very different numbers for neighboring nuclei. Com- panel is obtained assuming only allowed GT transitions. The paring TAGS measurements of the beta strength with dif- lower panel shows the comparison with calculations that also ferent models then becomes the only reliable validation include the first forbidden component. See more details in the method (see the 105Mo case discussed in the previous Sec- text. tion). Moreover it can give us hints on how to improve the nuclear structure calculations. Another example is related to the determination of very neutron-rich nuclei, up to the heaviest ones, that then neutron capture (n, γ) cross-sections for very exotic neutron- beta decay towards stability. About half of the observed rich nuclei, that also controls the nucleosynthesis flow in abundance of elements heavier than Fe in the Universe the r process. These are even more difficult to determine is synthesized in this way. The identification of the astro- experimentally because of the need to prepare suitable physical site where the process occurs is the subject of very targets. Direct measurements will require very imagina- active investigations. Core Collapse Supernovae were the tive techniques thus current efforts concentrate on indi- classical favoured site in spite of persistent difficulties met rect methods [155]. Theoretical estimates are based on when trying to reproduce observations with calculations. the statistical Hauser-Feshbach model [156] that uses av- On the other hand Neutron Star Mergers have recently be- erage quantities: nuclear level densities, photon strength come [151] a confirmed site for heavy element formation functions and neutron transmission coefficients. These are after the first observation of the gravitational waves gen- parameterized using data measured mostly close to stabil- erated and the analysis of the subsequent electromagnetic ity and consequently there is considerable uncertainty on radiation. Much remains still to be done in order to under- the values needed in r process calculations. stand the role of both scenarios combining astrophysical We have proposed a way to obtain experimental con- observations and calculations that require nuclear physics straints on the quantities that intervene in the Hauser- input (see [152] for a recent review). Feshbach estimate for very exotic neutron rich nuclei [12, Some of the key input parameters in r process cal- 24]. It is based on the analogy between radiative neutron culations are the decay properties of neutron-rich nuclei, capture reactions and the process of beta-delayed neutron more specifically half lives (T1/2) and beta-delayed neu- emission. The former depends mostly on Γγ and weakly tron emission probabilities (Pn) that control the nucle- on Γn and the latter can provide the ratio Γγ /Γn provided osynthesis flow. For such exotic nuclei the neutron sep- that we are able to measure the (expected weak) gamma A. Algora et al.: Beta-decay studies for applied and basic nuclear physics 23 emission from neutron unbound states. This is where the is mainly that of the shape of the photon strength func- sensitivity of the TAGS technique comes into play. The tion. main advantage of the method is that the measurements can be extended into regions quite far from stability. A closely related topic and also very interconnected with nuclear structure is the potential provided by beta In [12,24] the gamma-neutron competition was studied decay in relation to the study of collective phenomena. for the 87,88Br and 94Rb decays and more recently in [25] Beta decay could constitute a new means to investigate for 95Rb and 137I . The results are summarized in Table the presence and maybe some of the properties of low- 7, which shows Pγ , the gamma emission probability above lying collective modes, such as pygmy dipole modes pre- Sn defined by analogy with Pn (also shown). Observation dicted to appear at lower energies as nuclei become more of Table 7 reveals that in most of the cases Pγ is large, neutron rich. Collective modes are of crucial importance in 137 even larger than Pn. The large Pγ for I is confirmed by nuclear structure as they reflect the ability of the nucleons the TAGS measurement of [35]. The reason for this sur- to move coherently and provide insights into the proper- prising result is to be found in the nuclear structure of the ties of the nuclear force. The study of collective modes nuclei in the decay chain. A large mismatch between spin puts constraints on theoretical models as well. They are and parity of unbound states in the daughter nucleus and also the only observables that we can study on earth pro- the available states in the final nucleus means that neu- viding access to the intrinsic properties of nuclear mat- tron emission is hindered by the centrifugal barrier. Other ter, entering into the modelling of astrophysics phenomena measurements have also found large Pγ values in the decay like supernovae or neutron stars. Pygmy dipole resonances of 70Co [157] and 83Ga [158] and different nuclear struc- (PDR) could be the consequence of the appearance of neu- ture effects were invoked to explain it. This notable result tron skins in medium to heavy neutron-rich nuclei. The warns us about the neglect of gamma-neutron competition PDR might deliver information on neutron-star proper- in theoretical estimates of Pn (see also [159]), but does ties [160]. Important information on the equation of state not tell us about the statistical parameters of the Hauser- (EOS) of neutron-rich matter via strength-neutron-skin Feshbach model. The most interesting case from that point thickness correlation could be obtained [161]. of view is the decay of 94Rb where level densities in the daughter nucleus are large and neutron emission is not The presence of low-lying PDR could influence pro- hindered by angular momentum mismatch, making it a cesses of nucleosynthesis, especially (n,γ), (γ,n) reactions good test case for the statistical model. In this case gamma playing an important role in the r-process [162] as men- emission above Sn represents only 5% of neutron emission tioned earlier. Several questions remain unanswered about but even so it is more than one order-of-magnitude larger the collective modes when nuclei become more exotic. One than Hauser-Feshbach calculations using standard statis- limitation up to now has been the low intensity of the tical parameters. This is a challenging outcome. However accessible exotic beams which limits the possible stud- in order to translate a constraint in Γγ /Γn into a con- ies using standard nuclear or electromagnetic probes. In straint on (n, γ) cross-section we need additional informa- this context beta decay constitutes a new probe for low- tion. If we follow the assumption that extrapolating far lying collective modes. Further away from stability, as the from stability nucleon optical parameters (that determine energy window opened by beta decay increases, the en- Γn) is more reliable than extrapolating photon strength ergy of the pygmy modes decreases, allowing their exci- functions (that determine Γγ ) then this result would in- tation through the Gamow-Teller operator when the spin dicate one order-of-magnitude increase in the calculated and parity conservation conditions are fulfilled. Beta de- capture cross-section. Clearly more investigations are re- cay then offers new possibilities to study systematically quired and new TAGS measurements on suitable isotopes the presence of low-lying collective modes with the ex- are planned. isting exotic beam intensities. Our collaboration was first to propose an experiment on this topic [163]. Later on, A different method to obtain constraints on (n, γ) cross- the theoretical demonstration was provided by two mod- sections for unstable nuclei using TAGS measurements has els [158,164]. The quasi-particle model of [164] predicts been proposed by the NSCL group [37]. It was already that other components of the collective mode are excited mentioned in Section 2 in connection with the extraction through beta decay than those excited by the usual nu- of the branching ratio matrix, which is the first step of the clear and electromagnetic probes. In particular, beta de- Oslo method [38]. The goal of the Oslo method is to obtain cay would feed preferentially two-particle two-hole compo- the shape of the nuclear level density and photon strength nents of the collective mode, being thus complementary to function from the branching ratio matrix (in their termi- nuclear reactions. In the experimental results of [164] and nology: primary gamma ray intensities) and it was origi- [158], high resolution setups with a relatively small detec- nally applied to nuclear reaction experiments. Going from tion efficiency were used and the data may suffer from the a relative quantity (branching ratios) to absolute quanti- Pandemonium effect. The TAGS technique, using modern ties (photon strength functions and nuclear level densities) segmented spectrometers, seems to be very well adapted requires the use of normalization parameters coming from to tackle this problem, especially to evidence high energy external sources. In the case of beta decay TAGS mea- gamma-rays feeding the daughter ground state or the first surements away from the stability these are systematics, excited state. In parallel, ways to obtain experimental ev- extrapolations or theory. Thus the impact of this method idence of the collectivity of the states fed by beta decay, 24 A. Algora et al.: Beta-decay studies for applied and basic nuclear physics

Table 7. Pγ obtained from our measurements [24,25] in com- detectors adapted to the experimental conditions of such parison with the Pn values of the decays. Pγ is defined as the a facilities. From those facilities new and exciting results gamma emission probability above the Sn value (in analogy to will appear in the near future. Pn). The values are given in % (see the text for more details). This work has been supported by the Spanish Min- isterio de Econom´ıay Competitividad under Grants No. FPA2011-24553, No. AIC-A-2011-0696, No. FPA2014-52823- Isotope Pγ (T AGS) Pn C2-1-P, No. FPA2015-65035-P, FPA2017-83946-C2-1-P, No. 87 +0.49 Br 3.50−0.40 2.60(4) FPI/BES-2014-068222 and the program Severo Ochoa (SEV- 88 +0.27 Br 1.59−0.22 6.4(6) 2014-0398), by the Spanish Ministerio de Educaci´onun- 94 +0.33 Rb 0.53−0.22 10.18(24) der the FPU12/01527 Grant, by the European Commis- 95 +0.97 Rb 2.92−0.83 8.7(3) sion under the European Return Grant, MERG-CT-2004- 137 +1.84 I 9.25−2.23 7.14(23) 506849, the FP7/EURATOM contract 605203 and the FP7/ENSAR contract 262010, and by the Junta para la Ampliacion´ de Estudios Programme (CSIC JAE-Doc contract) co-financed by FSE. We acknowledge the support of STFC(UK) council grant which would not rely on theoretical predictions, should ST/P005314/1. This work was supported by the CNRS also be investigated. challenge NEEDS and the associated NACRE project, as well as the CHANDA FP7/EURATOM project (Contract No. 605203), and SANDA project ref. 847552, the CNRS/- 7 Summary, future and conclusions in2p3 PICS TAGS between Subatech and IFIC, and the CNRS/in2p3 Master projects Jyv¨askyl¨aand OPALE. Thanks In this article we have presented a review of the impact are also due to all collaborators who participated in the of our total absorption studies of beta decays that are measurements, to the IGISOL and University of Jyv¨askyl¨a relevant for reactor applications. The measurements pre- colleagues for their continous support and help and in par- sented have been performed at the IGISOL facility of the ticular to the PhD students and colleagues who worked in University of Jyv¨askyl¨aemploying the high isotopic pu- the analysis of the data and made this work possible (D. rity beams provided by the JYFL Penning Trap. These Jordan, E. Valencia, S. Rice, V. M. Bui, A. A. Zakari- measurements are not only relevant for the decay heat Issoufou, V. Guadilla, L. Le Meur, J. Briz-Monago and predictions and for the predictions of the reactor neutrino A. Porta). We also thank A. L. Nichols and T. Yoshida from reactors, but also provide results of interest for nu- for their support in the earlier stages of the work and P. clear structure and astrophysics. In particular they offer Sarriguren, A. Petrovici, K. L. Kratz, P. M¨ollerand col- the possibility of testing nuclear models in a more strin- laborators for providing theoretical calculations for some gent way and can provide additional information for the of the cases studied. Thanks are also due to A. Sonzogni estimation of (n,γ) cross sections of astrophysical interest and L. Giot for providing decay heat calculations and to for cases not directly accessible using reactions. M. Estienne for providing antineutrino summation calcu- Considerable progress has been made, but the ulti- lations. The work of J. Agramunt in the development of mate goal of the work presented in this article has not our data acquisition system used in all the experiments yet been reached. From the comparisons of the measured is acknowledged. Support from the IAEA Nuclear Data decay heat with the predictions of summation calcula- Section is acknowledged. tions, it is clear that there is still work to be done, in particular for the 235U fuel. The situation is similar in re- lation to the prediction of the antineutrino spectrum in 8 Authors contributions reactors, where the remaining discrepancies still require to measurements of a number of decays. Our collabora- All the authors were involved in the preparation of the tion is still working on these subjects and has approved manuscript. All the authors have read and approved the proposals to continue our studies at the IGISOL IV facil- final manuscript. ity in order to measure new decays that are important in the next relevant order. In this publication we have con- centrated mainly on the discussion of results obtained by References our collaboration, but other groups are also involved in similar research programmes at other facilities that pro- 1. W. Pauli letter to nuclear physicists in Tuebingen, Germany, vide experimental results relevant to the topics discussed 1930. here (see for example [35,101,102,157]). The upgrade and 2. E. Fermi, Il Nuovo Cimento, Volume 9, 1 (1934). advent of a new generation of radioactive beam facilities 3. J. C. Hardy et al., Phys. Lett. 71B, 307 (1977). like FRIB (Michigan, USA), RIBF (RIKEN, Japan), FAIR 4. Z. Hu et al., Phys. Rev C 62, 064315 (2000). (Germany), Spiral2 (France), etc. extends the possibili- 5. E. Nacher et al., Phys. Rev. Lett. 92, 232501 (2004). ties of TAGS measurements to more exotic domains than 6. E. Poirier et al., Phys. Rev. C 69, 034307 (2004). those offered by the present and future ISOL facilities. 7. A. Algora et al., Phys. Rev. Lett. 105, 202501 (2010). These measurements represent new challenges concerning 8. D. Jordan et al., Phys. Rev. C 87, 044318 (2013). the purity of the beams and require the development of 9. A. B. Perez-Cerdan et al., Phys. Rev. C 88, 014324 (2013). A. Algora et al.: Beta-decay studies for applied and basic nuclear physics 25

10. J. A. Briz et al., Phys. Rev. C 92, 054326 (2015). 50. M. Gupta et al., IAEA Report No. INDC(NDS) 0577 11. M. E. Estevez Aguado et al., Phys. Rev. C 92, 044321 (2010). (2015). 51. J. Ayst¨o,Nucl.¨ Phys. A 693, 477 (2001); I. D. Moore et 12. J. L. Ta´ın et al., Phys. Rev. Lett. 115, 062502 (2015). al., Nucl. Instrum. and Methods B 317, 208 (2013). 13. V. Guadilla et al., Phys. Rev. Lett. 122, 042502 (2019). 52. P. Dendooven, Nuclear Instruments and Methods in 14. C. L. Duke et al., Nucl. Phys. A151, 609 (1970). Physics Research B 126, 182 (1997). 15. B. Rubio et al., Journal of Phys. G: Nucl. Part. Phys. 31, 53. V. Kolhinen et al., Nuclear Instruments and Methods in S1477 (2005). Physics Research A 528, 776 (2004); T. Eronen et al., Eur. 16. B. Rubio et al., Journal of Phys. G: Nucl. Part. Phys. 44, Phys. J. A 48, 46 (2012). 084004 (2017). 54. J. Agramunt et al., Nucl. Data Sheets 120 , 74 (2014); J. 17. R. C. Greenwood et al., Nuclear Instruments and Methods Agramunt et al., EPJ Web of Conferences 146, 01004 (2017); in Physics Research A 390, 95 (1997). J. Agramunt et al., Nuclear Instruments and Methods in 18. M. Karny et al., Nuclear Physics A 640, 3 (1998). Physics Research A 807, 69 (2016). 19. J. L. Ta´ın and D. Cano-Ott, Nuclear Instruments and 55. A. Algora and J. L. Tain, ”Beta decay requirements for Methods in Physics Research A 571, 728 (2007) and Nuclear reactor decay-heat calculations: improving the prediction Instruments and Methods in Physics Research A 571, 719 power of fission products summation calculations”, Univ. of (2007). Jyv¨askyl¨aIGISOL I116 proposal (2006). 20. D. Cano et al., Nuclear Instruments and Methods in 56. B. Gomez, D. Cano, A. Algora and A. Jokinen, ”De- Physics Research A 430, 333 (1999). cay properties of beta delayed neutron emitters”, Univ. of 21. D. Cano et al., Nuclear Instruments and Methods in Jyv¨askyl¨aIGISOL I136 proposal (2008). Physics Research A 430, 488 (1999). 57. M. Fallot, J.L Tain and A. Algora, ”Study of nuclei rel- 22. V. Guadilla et al., Nuclear Inst. and Methods in Physics evant for precise predictions of reactor neutrino spectra”, Research, A 910, 79-89 (2018). Univ. of Jyv¨askyl¨aIGISOL I153 proposal (2009). 58. A. Algora and J. L. Tain, ”Total absorption measurement 23. J. L. Ta´ın et al., Nuclear Instruments and Methods in 100 Physics Research A 774, 17 (2015). of the beta-deacy of Tc”, Univ. of Jyv¨askyl¨aIGISOL I154 24. E. Valencia et al., Phys. Rev. C 95, 024320 (2017). proposal (2009). 25. V. Guadilla et al., Phys. Rev. C 100, 044305 (2019). 59. A. Negret and B. Singh, Nucl. Data Sheets 124, 1 (2015). 26. K.-L. Kratz et al., Z. Phys. A 306, 239 (1982). 60. S. Goriely, F. Tondeur, and J. Pearson, At. Data Nucl. 27. D. Abriola and A. A. Sonzogni, Nucl. Data Sheets 107, Data Tables 77, 311 (2001); P. Demetriou and S. Goriely, 2423 (2006). Nucl. Phys. A 695, 95 (2001). 61. R. Capote et al., Nucl. Data Sheets 110, 3107 (2009); 28. J. L. Ta´ın et al., J. Korean Phys. Soc. 59, 1499 (2011). https://www-nds.iaea.org/RIPL-3/ 29. A. Algora, ATOMKI Annual Report 2004, p. 17 (2004). 62. S. Rice et al., Phys. Rev. C 96, 014320 (2017). 30. J. L. Ta´ın et al., Nuclear Instruments and Methods in 63. S. Rice, PhD thesis, University of Surrey, 2014. Physics Research A 803, 36 (2015). 64. A. Sonzogni, private communication. 31. M. Karny et al., Nuclear Instruments and Methods in 65. R. C. Greenwood et al., Nuclear Instruments and Methods Physics Research A 836, 83 (2016). in Physics Research A 314, 514 (1992) 32. L. Batist, private communication. 66. J. L. Ta´ınand A. Algora, IFIC-06-1 Report, 2006. 33. D. Jordan, PhD thesis, Univ. of Valencia, 2010. 67. A. A. Zakari-Issoufou et al., Phys. Rev. Lett. 115, 102503 34. A. Simon et al., Nuclear Instruments and Methods in (2015). Physics Research A 703, 16 (2013). 68. A. Tobias, CEGB Report No. RD/B/6210/R89, (1989). 35. B. C. Rasco et al., Phys. Rev. C 95, 054328 (2017). 69. J. K. Dickens et al., Nucl. Science and Eng. 74, 106 (1980) 36. B. C. Rasco et al., JPS Conf. Proc. 6, 030018 (2015). and J. K. Dickens et al. Nucl. Science and Eng. 78, 126 37. A. Spyrou et al., Phys. Rev. Lett. 113, 232502 (2014). (1981). 38. M. Guttormsen et al., Nucl. Instrum. Methods Phys. Res., 70. L. Giot (Subatech Lab., Nantes, France) private commu- Sect. A 255, 518 (1987). nication. 39. A. C. Dombos et al., Phys. Rev C 93, 064317 (2016). 71. C. L. Jr. Cowan, F. Reines, et al., Science 124, 103 (1956). 40. V. Guadilla, Ph.D. thesis, University of Valencia, 2017. 72. L.A. Mikaelian, 1977, Proc. Int. Conf. Neutrino-77, v. 2, 41. V. Guadilla et al., Phys. Rev C 96, 014319 (2017). p. 383. 42. P. Huber and P. Jaffke, Phys. Rev. Lett. 116, 122503 73. Y. Abe et al., Phys. Rev. Lett. 108, 131801 (2012). (2016). 74. F. P. An et al., Phys. Rev. Lett. 108, 171803 (2012). 43. M. F. James, Journal of Nucl. Energy 23, 517 (1969). 75. J. K. Ahn et al., Phys. Rev. Lett. 108, 191802 (2012). 44. K. Way and E. Wigner, Phys. Rev. 73, 1318 (1948). 76. A. Cucoanes et al., arXiv:1501.00356. 45. G. Rudstam et al., At. Data Nucl. Data Tables 45, 239 77. K. Schreckenbach et al., Phys. Lett. 99B, 251 (1981). (1989). 78. K. Schreckenbach et al., Phys. Lett. 160B, 325 (1985). 46. O. Tengblad et al., Nucl. Phys. A 503, 136 (1989). 79. F. von Feilitzsch, A. A. Hahn and K. Schreckenbach, Phys. 47. ENSDF, http://www.nndc.bnl.gov/ensdf Lett. 118B, 162 (1982). 48. T. Yoshida, A. L. Nichols et al., Assessment of Fis- 80. A. A. Hahn et al., Phys. Lett. B 218, 365 (1989) . sion Product Decay Data for Decay Heat Calculations 81. T. A. Mueller et al., Phys. Rev. C 83, 054615 (2011). (OECD/NEA Working Party for International Evaluation 82. P. Huber, Phys. Rev. C 84, 024617 (2011). Co-operation, Paris, 2007), NEA report NEA/WPEC-25 83. G. Mention et al., Phys. Rev. D 83, 073006 (2011). (2007) 1., Vol. 25 (NEA No. 6284). 84. L. N. Kalousis and SoLid collaboration, J. Phys.: Conf. 49. A. L. Nichols, IAEA Report No. INDC(NDS) 0499 (2006). Ser. 888, 012181 (2017). 26 A. Algora et al.: Beta-decay studies for applied and basic nuclear physics

85. H. Almaz´an et al. (STEREO Collaboration), Phys. Rev. 123. K. S. Krane, Introductory Nuclear Physics (Wiley, New Lett. 121, 161801 (2018). York, 1988). 86. J. Ashenfelter et al., Phys. Rev. Lett. 122, 251801 (2019). 124. R. D. Evans, The Atomic Nucleus (McGraw-Hill, New 87. G. Mention et al., Phys. Lett. B 773 (2017) 307, York, 1956). arXiv:1705.09434. 125. K. Siegbahn, Alpha, Beta and Gamma Ray Spectroscopy 88. W. Mampe et al., Nucl. Instrum. Meth. 154, 127 (1978). (North-Holland, Amsterdam, 1966). 89. A. Onillon, ”Updated Flux and Spectral Predictions Rel- 126. M. Ichimura, H. Sakai and T. Wakasal Prog. Part. Nucl. evant to the Reactor Antineutrino Anomaly”, Applied An- Phys 56, 451 (2006). tineutrino Physics Workshop 2018, (2018). 127. G. Martinez-Pinedo, A. Poves, E. Caurier and A. P. 90. A. C. Hayes, J.L. Friar, G.T. Garvey, G.Jungman, G. Zuker, Phys. Rev. C 53, R2602 (1996). Jonkmans, Phys. Rev. Lett. 112, 202501 (2014). 128. P. Gysbers et al., Nature Physics 15, 428 (2019). 91. D. L. Fang and B. A. Brown, Phys. Rev. C 91, 025503 129. I. S. Towner. Nucl. Phys. A 444, 402 (1985). (2015). 130. K.H. Burkard et al., Nucl. Instrum. Methods 139, 275 92. L. Hayen, J. Kostensalo, N. Severijns, and J. Suhonen, (1978). Physical Review C 100, 054323 (2019). 131. M. Karny et al., Nucl. Instr. Methods B 126, 411 (1997). 93. X.B. Wang, J.L. Friar and A.C. Hayes, Phys. Rev. C 94, 132. C. Plettner et al., Phys. Rev. C 66, 044319 (2002). 034314 (2016). 133. Z. Hu et al., Phys. Rev. C 60, 024315 (1999). 94. A. Hayes, contribution to the Solvay workshop (2017). 134. A. Algora et al., Phys. Rev. C 70, 064301 (2004). 95. R. W. King and J. F. Perkins, Phys. Rev. 112, 963 (1958). 135. A. Algora et al., Phys. Rev. C 68, 034301 (2003). 96. F. T. Avignone et al. , Phys. Rev. 170, 931 (1968). 136. D. Cano-Ott, Ph.D. thesis, University of Valencia, 2000. 97. P. Vogel, G. K. Schenter, F. M. Mann and R. E. Schenter, 137. E. Nacher et al., Phys. Rev. C 93 014308 (2016). Phys. Rev. C 24, 1543 (1981). 138. C. B. Hinke et al., Nature 496, 341 (2012). 98. N. Haag et al., Phys. Rev. Lett. 112, 122501 (2014). 139. D. Lubos et al., Phys. Rev. Lett. 122, 222502 (2019). 99. M. Fallot et al., Phys. Rev. Lett. 109, 202504 (2012). 140. A. Algora and B. Rubio, ” Studies of the beta decay of 100. A. A. Sonzogni, T. D. Johnson, and E. A. McCutchan, 100Sn and its neighbours with a Total Absorption Spectrom- Phys. Rev. C 91, 011301(R) (2015). eter (TAS)”, RIKEN proposal NP1612-RIBF147 (2016). 101. B. C. Rasco et al., Phys. Rev. Lett. 117, 092501 (2016); 141. A. Algora et al., RIKEN Progress Report 2019, in print. 102. A. Fijalkowska et al., Phys. Rev. Lett. 119, 052503 (2017). 142. L. Batist et al., Eur. Phys. J. A 46, 45 (2010). 103. P. Dimitriou and A. L. Nichols, IAEA report 143. I. Hamamoto and X. Z. Zhang, Z. Phys. A 353, 145 INDC(NDS)-0676, Feb. 2015, IAEA, Vienna, Austria (1995). 104. D. A. Dwyer and T. J. Langford, Phys. Rev. Lett. 114, 144. P. Sarriguren et al., Nucl. Phys. A 635, 55 (1998); P. 012502 (2015). Sarriguren et al., Nucl. Phys. A 658 13 (1999); P. Sarriguren 105. JEFF and EFF projects et al., Nucl. Phys. A 691, 631 (2001). http://www.oecdnea.org/dbdata/jeff/, URL 145. A. Petrovici, A. Schmid and A. Faessler, Nucl. Phys. A http://www.oecd-nea.org/dbdata/jeff/. 665 333 (2000). 106. D. Brown et al., Nucl. Data Sheets 148, 1 (2018). 146. V. Guadilla et al., Phys. Rev. C 100, 024311 (2019). 107. M. Estienne (Subatech lab., Nantes, France) private com- 147. V. Guadilla et al., in preparation. munication. 148. P. Sarriguren, private communication. 108. F. P. An et al. (Daya Bay Collaboration), Phys. Rev. 149. K. L. Kratz and P. M¨ollerprivate communication. Lett. 118, 251801 (2017). 150. D. Jordan et al. in preparation. 109. A. C. Hayes et al., Phys. Rev. Lett. 120, 022503 (2018). 151. D. Watson et al., Nature 574, 497 (2019). 110. M. Estienne et al., Phys. Rev. Lett. 123, 022502 (2019). 152. C. J. Horowitz et al., J. Phys. G: Nucl. Part. Phys. 46, 111. T. Yoshida, T. Tachibana, S. Okumura, and S. Chiba, 083001 (2019). Phys. Rev. C 98, 041303(R) (2018). 153. J.L. Tain et al., Acta Phys. Polonica B 49, 417 (2018). 112. P. Vogel and J. F. Beacom, Phys. Rev. D 60 (4), 053003 154. R. Caballero-Folch et al., Phys. Rev. Lett. 117, 012501 (1999). (2016). 113. F. P. An et al., Chinese Phys. C 41, 013002 (2017). 155. A.C. Larsen et al., Prog. Part. Nucl. Phys. 107, 69 (2019). 114. Y.J. Ko et al., Phys. Rev. Lett. 118, 121802 (2017). 156. W. Hauser and H Feshbach, Phys. Rev. 87, 366 (1952). 115. B. Achbar et al., Phys. Lett. B 374 243 (1996). 157. A. Spyrou et al., Phys. Rev. Lett. 117, 142701 (2016). 116. H. de Kerret et al., Nat. Phys. 16, 558 (2020). 158. A. Gottardo et al., Physics Letters B772, 359 (2017). 117. J. M. Berryman and P. Huber, Phys. Rev. D 101, 015008 159. M. R. Mumpower et al., Phys. Rev. C 94, 064317 (2016). (2020). 160. C. J. Horowitz et al., Phys. Rev. Lett. 86, 5647 (2001). 118. A. A. Sonzogni et al., Phys. Rev. C 98, 014323 (2018). 161. J. Piekarewicz, Phys. Rev. C 73 044325 (2006). 119. E. Ciuffoli, J. Evslin and X. Zhang, Phys. Rev. D 88 (3) 162. S. Goriely, Phys. Lett. B 436, 10 (1998). 033017 (2013). 163. M. Fallot, A.Porta, A. Algora, B. Rubio and J.-L. Tain, 120. An F et al., J. Phys. G: Nucl. Part. Phys. 43 030401 ”Total Absorption Spectroscopy for Nuclear Structure, Nu- (2016). clear Astrophysics, Neutrino and Reactor Physics”, ALTO 121. D. Akimov et al., Science Vol. 357, Issue 6356, 1123 facility Proposal Ref. N-RI-6 (2014). (2017). 164. M. Scheck et al., Phys. Rev. Lett. 116, 132501 (2016). 122. B. Rubio and W. Gelletly, Beta Decay of exotic nuclei The Euroschool Lectures on Physics with Exotic Beam Vol III (Springer Lecture Notes in Physics vol 764, year 2009, p- 99) ed. J.S. Al-Khalili and E. Roeckl (Berlin Springer).